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Talk:Schrödinger equation
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Outline of Schrödinger equation for different levels
High school
- 1 Schrödinger field theory vs Graviton
- 2 Heisenberg picture versus Schrödinger picture
- 3 Atomic weight versus atomic number
- 4 Introductory Preamble
- 5 Separate article on exact solutions?
- 6 "Incorrect - why?"
- 7 Partial waves method
- 8 I'm not a physicist
- 9 Article gives impression that the relativistic forms are also called the Schrödinger equation
- 10 Fails to Specify Variables
- 11 Axiomatic construction using time-evolution operator
- 12 Distance and potential confused in Constant Potential section
- 13 "Derived from symmetry principles"??
- 14 "Simultaneous Positions"
- 15 "Schrödinger Derivation"
- 16 "Only One Wave Equation"
- 17 r in the equations goes undefined
- 18 Equation boxes
- 19 Multiverse
Schrödinger field theory vs Graviton[edit]
Schrödinger field theory handles particles as part of the same wavefunction, and time degrades distance in order the spin of the particles is maintained. Particles are treated as "sacks of noise spots" a discrete mathematics approach. No extra particles needed, but in order the Schrödinger Equation describes all particles as parts of the same wider and complex wavefunction, particles should be considered as "noise sacks". Discrete mathematics and combinatorics needed to express the "entropic degradation of distance due to time" and the overall urge of achieving a "mean inner time perception of the particles of a gravitational system" — Preceding unsigned comment added by 184.108.40.206 (talk) 07:17, 30 May 2015 (UTC)
Heisenberg picture versus Schrödinger picture[edit]
Currently, the subsection Schrödinger equation#Matrix mechanics and the Schrödinger picture makes it appear wrongly that the equation
is universally true and consistent with the Schrödinger equation. On the contrary, that equation is only true in the Heisenberg picture (and then only when the partial derivative of A wrt time is zero) while the Schrödinger equation is only true in the Schrödinger picture. Although the two pictures give the same physical results, they are mathematically inconsistent with each other. (They use different bases for the Hilbert space as a function of time.) So any calculation should be done entirely in just one of the two pictures. This article should state at the outset that the Schrödinger equation is part of the Schrödinger picture, not the Heisenberg picture. JRSpriggs (talk) 09:34, 15 March 2012 (UTC)
- I just moved this to Matrix mechanics without realizing this comment - sorry. -- F=q(E+v×B) ⇄ ∑ici 09:21, 17 March 2012 (UTC)
Atomic weight versus atomic number[edit]
Could you explain to me why atomic number Z is used in the equation in section Schrödinger equation#Two-electron atoms or ions in the kinetic energy term (and the formula for the reduced mass) rather than mass number A (or, more precisely, the mass of the nucleus as a whole including neutrons as well as protons divided by the mass of a proton)? Of course, Z is appropriate in the potential energy term. JRSpriggs (talk) 20:07, 3 April 2012 (UTC)
- Zmp is the mass of the nucleus, mp is the mass of the proton. For 2-electron atoms mentioned there would be Z protons and... some neutrons. You're right. Lets replace with just M for the mass of the nucleus. F = q(E+v×B) ⇄ ∑ici 20:18, 3 April 2012 (UTC)
- Out of interest, isn't the reduced mass usually mu , not the obscure ? I have yet to see that in a source and arn't we supposed to be using the most common notation? Maschen (talk) 21:14, 3 April 2012 (UTC)
Introductory Preamble[edit]
I wanted to say something like:-
"Like Newton's second law Schrödinger's equation for a quantum system has not been proved or derived from more elementary principles. It is used because it works and has predicted a multitude of reactions time and time again - the only proof is in nature or natural." Blueawr (talk) 07:55, 1 September 2012 (UTC)
- You could put that in somewhere, but it is the kind of statement that needs to be backed up with a good secondary source. RockMagnetist (talk) 16:53, 1 September 2012 (UTC)
Separate article on exact solutions?[edit]
I have proposed before (in passing) that we make an article on the exact solutions (and forgot, till now), such as Schrödinger equation (exact solutions), because;
- it will trim the article (currently 81.527 kB, too big)
- reduces the amount of maths in this article, allowing for more qualitative content future editors may add,
- parallels the nice idea of Exact solutions in general relativity from Einstein field equations,
- helpful for those just introduced to the equation, since there will not be many realistic systems it can be solved for exactly, and serves as a springboard to perturbation theory (quantum mechanics), variational method (this article is for QM), ladder operators...
written summary style for detailed articles on specific systems (step potential, delta potential, Harmonic oscillator (quantum), hydrogen atom etc.). Any objections? Maschen (talk) 09:59, 11 November 2012 (UTC)
- Update: I'm drafting this in a pre-article (in namespace), it will not be created if people desire to re-merge in the future... Maschen (talk) 18:11, 1 December 2012 (UTC)
"Incorrect - why?"[edit]
Incorrect in that it doesn't detail the whole situation which would require something to be going faster when it is lower than when it is higher. Consider that a SR71 could be higher and be going faster (than I am), and you'll see why the statement is wrong. I think removal of the line is appropriate. --Izno (talk) 00:48, 6 December 2012 (UTC)
- We're talking about the sentence "For example, a frictionless roller coaster has constant total energy; therefore it travels slower (low kinetic energy) when it is high off the ground (high gravitational potential energy) and vice versa." Right?
- I read this as a statement about frictionless roller coasters, and I believe it is a correct statement about frictionless roller coasters. It seems to me that readers are unlikely to read this sentence and get the impression that it is true in any context besides frictionless roller coasters.
- But maybe I'm wrong. So here is an idea:
- "For example, a free, frictionless roller coaster has constant total energy; therefore this roller coaster will travel slower (low kinetic energy) when it is high off the ground (high gravitational potential energy) and vice versa." --Steve (talk) 16:20, 6 December 2012 (UTC)
- I read it for what it was, and that it was trying to convey an example of conservation of energy. Your change makes it slightly better. But connecting a roller coaster to the law needs more; the assumptions are not laid out which would make the statement precisely true. On top of this, it still does not illustrate why it is the case that the roller coaster will travel faster in a different place. What is needed, quite frankly, is a link to the conservation of energy article. I still favor deletion of the line and would favor insertion of a link to the law of conservation of energy, which is quite oddly lacking for the first time that implications are discussed in the article. (Perhaps because it is used as a part of the assumptions section?) --Izno (talk) 17:11, 6 December 2012 (UTC)
- In other words, it is not clear to me the connection. "It goes fast here and slow here" doesn't make it clear to a reader why that is the case, only that it is the case. --Izno (talk) 17:24, 6 December 2012 (UTC)
- As the one who reverted, it should be clear that potential energy and kinetic energy interchange and the sum of these is constant assuming no dissipative effects (e.g. friction, heating). The worded equation is given there, no?. If the PE increases (for gravity, increase in altitude is one way) then the KE decreases (speed decreases by the square root), and vice versa. The aeroplane you linked to has nothing to do with roller coasters and frictionless systems so I have no clue why you point to that... Maschen (talk) 18:00, 6 December 2012 (UTC)
- According to archive 3, the roller coaster example was added to analogize a familiar system (or at least one that is easy to understand) with a particle in a potential, i.e. the roller coaster tends to move in directions of decreasing potential, and there are stable/unstable equilibrium points. If you're finding this example confusing - maybe there is no harm in removing it... but it's not complicated... Maschen (talk) 18:07, 6 December 2012 (UTC)
- I added the link conservation of energy in the first sentence of that section. Better? Maschen (talk) 20:23, 6 December 2012 (UTC)
Naturally, but this is only true for an object in motion with only one force (and conservative at that) acting upon it (or if there is a second force, it is a normal force and does not counteract completely the first force). I point to an airplane because it is a system which goes high and fast, which makes it a problematic counterexample to our example of a roller coaster. In effect, the comment of "high and slow" is so basic as to be useless, because it does not lay out the requisite assumptions.
If it is our desire to comment on the fact that systems act toward states with a lower potential, then the example certainly does not convey that.
The thought I had was to switch it with a pendulum, or a vibrating string. It's not uncommon to see either of the two in context of wave equations (in general). (I'll note that a pendulum is probably better for this example.) Even so, switching the type of system would not sufficiently fix the problem of the original statement. --Izno (talk) 20:38, 6 December 2012 (UTC)
- Now I see what you are trying to say (except for when you said the example was wrong when it isn't, but we're past that now). Apologies... Perhaps it is too short to be fully understandable. The pendulum (or the like) sounds like a nice idea. Let's see what others think... Maschen (talk) 21:06, 6 December 2012 (UTC)
- Actually (you'll like this), maybe the example could just be deleted since it only serves as an example of classical energy conservation in a specific case, suppose there is no loss of continuity. Up to others from this point on, I'll stay out of this... Maschen (talk) 21:16, 6 December 2012 (UTC)
Partial waves method[edit]
Something should be mentioned concerning the use of the equation to scattering problems by partial wave analysis.--22.214.171.124 (talk) 12:31, 2 August 2013 (UTC)
- I don't agree. Of cause it is true that the Schroedinger equation is the basis of scattering theory. But this is true for basically any quantum mechanical problem. There is no point in listing all problems that build on this equation. Ciao. --Falktan (talk) 16:52, 26 August 2013 (UTC)
I'm not a physicist[edit]
Hey guys. I was curious about learning more about the cat in a box I heard and this page is really thick. You need a knowledge of quantum physics just to read the article. Any chance we can dumb it down for the lay person? — Preceding unsigned comment added by 126.96.36.199 (talk) 13:08, 12 August 2013 (UTC)
- Maybe it needs something, somewhere, but this article is about physics. The "cat in a box business" was intended to make a serious point, but Schrödinger was a person who wrote ironically and sometimes sarcastically. His writings are frequently not to be taken exactly at face value. It may help to know that he disliked cats. It appears that his initial idea was to ridicule some of the early and emerging conclusions of the Copenhagen group by saying, in effect, "If you believe this bleep then you would have to accept the idea of a cat smooshed out in some state neither alive nor dead but in some sense both." Then, as the months and years rolled on, it became clear that electrons turned in both counterclockwise and clockwise rotation at the same time, and many other kinds of "superposition" could be demonstrated. Then, going back to the cat example, if you really did try to do the experiment, what would that mean? It turns out that the original quip left out a lot of detail that has been funneled together into the idea of decoherence. The original idea was that if nobody observes the geiger counter that is linked to a release mechcanism for the poison gas, then the geiger counter doesn't do anything, so the cat and everything in the box is suspended until a human being (delusions of grandeur here) opens the box and makes an observation. Who says that the cat cannot be aware of the geiger counter either clicking or not clicking? Who says that "observation" has to mean the report of stimuli received in human eyes or ears to brain tissue that processes the report somehow and concludes "the geiger counter has (not yet) clicked." Why won't a rolling movie camera in with the cat record the flickering needle of the geiger counter just as well? Why won't anything else that is done by being connected to the needle or the guts of the geiger counter serve just as well as an observation? And blah, blah, blah. You can't boil it down to a paragraph without making it into a dogmatic assertion that anybody with good sense should be suspicious of. The best you could do would be to say that Dr. Big explained/defined it that way ex cathedra. But it is, at heart, a big, complicated discussion. P0M (talk) 18:39, 12 August 2013 (UTC)
- The "cat in a box" was supposed to illustrate the concept that two "impossible states" simultaneously occur (i.e.wavefunction) before one or the other does happen (as in wavefunction collapse).
- Unfortunately, it seems one does need some exposure to the very basics of QM before the SE is introduced in most courses/textbooks I've seen, mainly in wave-particle duality which the article already does include, but given that it's a crucial aspect of QM (indeed a fundamental postulate) maybe we need to alter the background QM. For now, not sure how rewrite... M∧Ŝc2ħεИτlk 19:09, 12 August 2013 (UTC)
- Note that there is an article on Schrödinger's cat. RockMagnetist (talk) 02:12, 13 August 2013 (UTC)
- Regarding the above comment that 'it became clear that electrons could turn clockwise and anti-clockwise at the same time'. This is not true. Quantum mechanics expressly prohibits simultaneous values in its fundamental postulates. The common confusion on this point is that a quantum state represented by say |up> is one to one with the probability P(up) not with the actual value 'up'. Additional, the '+' sign is not an addition, it is a probability 'OR' operator. The confusion lies in that classical mechanics deals and writes expression/relations of the variables directly, such as position x and momentum p. Quantum mechanics only deals and writes expressions, effectively, dealing only with probabilities such as P(x) and P(p). One has to know what the symbols in say, |psi> = a|up> + b|dn> mean. It means a|up> OR b|dn>. For example, in Boolean logic 1 + 1 is still 1 not two. A state in QM is a probability distribution of a position, not an actual position. Kevin Aylward 17:01, 11 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
Article gives impression that the relativistic forms are also called the Schrödinger equation[edit]
I have not read through this thoroughly, but noticed the following that might confuse a reader:
- The lead gives no indication that the domain of applicability of the Schrödinger equation is strictly the nonrelativistic domain. In fact, it says that it can be transformed into the Feynman path integral formulation, and since the latter is relativistic (I'm not even aware that it has any nonrelativistic form), I would go so far as to suggest that this is seriously misleading.
- The article discusses both nonrelativistic and relativistic wave equations, giving the impression that the name "Schrödinger equation" encompasses them all. My understanding is that it refers strictly to the nonrelativistic equations given early on, and that the Dirac equation and the Klein–Gordon equation are not considered to be examples of the Schrödinger equation.
- The subsections on time-dependent and time-independent equations would be better named for the respective forms of the Hamiltonian, not the resultant form of the equation, e.g. General Hamiltonian and Time-independent Hamiltonian. They could also be written to emphasise that with a time-independent Hamiltonian (which in itself is generally inherently an approximation) the equation can take another form
My involvement, time and expertise in this sort of article is not sufficient to make such edits, but I hope any who are suitably interested would like to use these pointers as inputs to their edits. — Quondum 06:30, 23 September 2013 (UTC)
- The Schro eqn is a fundamental postulate of QM, and the article states the general equation can be used in relativistic and non-relativistic context (yes, it can, all that's needed is the correct Hamiltonian), if this were not the case then how can non-relativistic QM and RQM be consistent with the postulates of QM?
- Feynman path integrals are equivalent to the Schrodinger equation, and can be relativistic or non-relativistic (there is a connection between non-relativistic QM and classical mechanics... the correspondence principle). There is plenty literature on Feynman path integrals, but I don't have any to hand right now. For a WP pointer, this section in the path integral formulation article uses the classical kinetic energy expression.
- A "general Hamiltonian" is time-dependent in general anyway, and is more meaningful than "general" and provides contrast with "time-independent".
- M∧Ŝc2ħεИτlk 05:59, 24 September 2013 (UTC)
- The article says "The general form of the Schrödinger equation is still applicable, but the Hamiltonian operators are much less obvious, and more complicated." Such an equation strikes me as highly contrived; for example, the Hamiltonian needed to obtain the Klein–Gordon equation would be really strange, and the Dirac equation cannot be considered to be a Schrödinger equation, as the Dirac equation is in terms of matrices, and the Schrödinger equation in terms of real values. Is this really in sources?
- I'll accept what you say about Feynman path integrals. — Quondum 01:23, 25 September 2013 (UTC)
- Yes, the Dirac equation can be considered a Schro equation, Penrose says this in the chapter on the Dirac equation (page 621 in my copy "the Dirac equation can be written in the form of a Schro equation ... Of course the singling out of the time derivative is not relativistically invariant but the entire Dirac equation is"). Particle physics books (many are listed in the RQM article references, the one I have to hand now is Particle physics by B.R. Martin and G. Shaw) usually say something like "Dirac proposed a Hamiltonian of the form:
- where a = α1, α2, α3 and β are to be found subject to the constraints..."
- While non-relativistic quantum Hamiltonians are just functions of position, momentum, and time (as in classical Hamiltonian mechanics), the relativistic quantum Hamiltonians are also functions of position, momentum, time, and spin matrices. The Schro equation does not restrict the wavefunction to be a scalar, it could be anything that can describe quantum mechanics.
- You have a point about the KG Hamiltonian, most people don't derive it from the Hamiltonian since it can be derived directly from the energy-momentum relation or viewed as the square of the Dirac equation (you knew that), but I'm sure it's possible one way or another. I'll look for sources.
- M∧Ŝc2ħεИτlk 07:37, 25 September 2013 (UTC)
- Yes, the Dirac equation can be considered a Schro equation, Penrose says this in the chapter on the Dirac equation (page 621 in my copy "the Dirac equation can be written in the form of a Schro equation ... Of course the singling out of the time derivative is not relativistically invariant but the entire Dirac equation is"). Particle physics books (many are listed in the RQM article references, the one I have to hand now is Particle physics by B.R. Martin and G. Shaw) usually say something like "Dirac proposed a Hamiltonian of the form:
- By the way, a good faith edit was made to the RQM section of this article saying QM is formulated to be consistent with SR. As YohanN7 confirmed a while back (see talk:relativistic quantum mechanics#Suggestions): RQM = SR + QM, i.e. special relativity and quantum mechanics applied together. The statement "Quantum mechanics formulated to be consistent with special relativity" may have the implication that QM is modified in some way (or may not...). Quantum mechanics doesn't actually change, all pictures of QM are already applicable with SR, but the outcome is that new predictions and mathematical objects appear, which did not from QM alone. M∧Ŝc2ħεИτlk 07:56, 25 September 2013 (UTC)
- I suppose the Schrödinger equation evolved rather than being replaced. This is in accordance with the physicist's natural approach of "if it works, use it", in contrast with the mathematician's more rigorous approach. Given that the Schrödinger equation can be adapted to both Galilean and special relativity (and no doubt anything else), that the wavefunction and the underlying abstract algebra is regarded as being free in type, and that the Hamiltonian is unconstrained (it presumably becomes only loosely representative of energy), the Schrödinger equation is essentially not falsifiable, which is not a pretty state of affairs. It asserts that there exists some wavefunction, which when subject to some operator (which is expressed as the difference between the "Hamiltonian" and the partial derivative with respect to time multiplied by a constant), yields zero. More strictly interpreted, it says that the wavefunction is the solution of a homogenous differential equation, or equivalently that it obeys the superposition principle - and nothing else whatsoever. Beyond this, anything to be added is freely chosen in the choice of abstract algebra and Hamiltonian.
- On my edit, I have reverted it since as you suggest, there should not be a suggestion of reformulation of QM, only that its form is constrained to be relativistically invariant. I am not particularly comfortable with "applied together", due to what I perceive as a semantic difference between "applied together" and "simultaneously apply". The former is an active form, suggesting a process in which one takes QM, and then applies SR, getting something new. The latter is a passive form, indicating that they both are part of the framework, i.e. they act as constraints. Would this change make more sense? — Quondum 09:53, 25 September 2013 (UTC)
- The second change, for the RQM section, seems fine with me.
- Remember the Schrodinger equation is a postulate of quantum mechanics, assumed to be true, so it could be falsified (just like the postulates of special/general relativity) if there was some experimental phenomenon which the SE cannot describe (the Hamiltonian for the phenomenon is impossible to obtain or just pathologically unphysical).
- The article states:
- This is the equation of motion for the quantum state. In the most general form, it is written:
- This is the equation of motion for the quantum state. In the most general form, it is written:
- With no constraint on the Hamiltonian other than it be a linear operator field over time and space, or on the underlying algebra other than that it be compatible with complex scalar multiplication, the general Schrödinger equation can be rewritten as
- for an arbitrary linear operator .
- This is why I said what I said before: with no further constraints, one can deduce linearity, but nothing else. The only way of falsifying this equation is if linearity does not apply, and I don't think that linearity is in contention. If there are some constraints on (equivalently the Hamiltonian), for example that it obeys some conditions (e.g. locality, which would manifest as the operator being expressible in terms of partial derivatives with respect to the space and time coordinates), the equation would assert more than superposition. For the Galilean and special relativity cases, further constraints would apply. Even so, it is still saying very little until one adds yet further constraints, such as conservation of energy and momentum. So, I hope you can see that pretty much everything that can be "deduced" (including that it is an equation of continuity/evolution) must be built into the form of (or constraints on) the Hamiltonian. — Quondum 12:12, 25 September 2013 (UTC)
- The article states:
- Yes, I do know that constraints are needed on the Hamiltonian in the context to construct it using physical principles, but I'm still not 100% sure what you're trying to get at improving the article...
- OK... This article already gives the construction for the non-relativistic Hamiltonian, for one and n particles in any potential, we can agree on that. Are you saying to discuss the Hamiltonian (with constraints) for other situations in this article, like for the Pauli equation, and relativistic wave equations in general? We could always rewrite the article in some places (maybe have a section on this after some reorganizing), linking to the remaining details in the Hamiltonian operator article.
- I apologize for misunderstanding... M∧Ŝc2ħεИτlk 19:33, 25 September 2013 (UTC)
- I need to review the article in more detail to make specific suggestions, which I will be able to do more sensibly now that you have disabused me of some of my preconceptions. I should then be able to make more specific suggestions. — Quondum 21:43, 25 September 2013 (UTC)
Split off the non-relativistic content to another article(s)?[edit]
In response to the above thread...
I proposed before (more than once now) to transfer the exact solutions of the Schro eqn to a separate article Schrödinger equation (exact solutions). Note also the main article quantum mechanics has overlap on exact solutions to the non-relativistic Schro equation. Would cutting out the "exact solution" sections in this article and the QM article be useful?
Or instead, we could just transfer all of the non-relativistic formalism to another article: Schrödinger equation (non-relativistic) (by all means correct me on the dashes, this is just a suggestion...). This may have been proposed by someone before also...
Maybe both? In Schrödinger equation (non-relativistic), we have a discussion of the general ideas of the non-relativistic case, leading onto the mathematical details (such as those in the "properties" section of this article), without the exact solutions, then linking to the Schrödinger equation (non-relativistic) article.
Any thoughts? M∧Ŝc2ħεИτlk 20:36, 25 September 2013 (UTC)
- Update: see also this section. M∧Ŝc2ħεИτlk 12:51, 27 September 2013 (UTC)
- I just realized there is the article List of quantum-mechanical systems with analytical solutions. So there is no need for a new article. M∧Ŝc2ħεИτlk 09:16, 27 January 2014 (UTC)
Fails to Specify Variables[edit]
In a lot of the equations it doesn't specify the meanings of all the variables. This isn't "quantum physics experts we already know all this" wiki. Every variable should be specified as to what it means.188.8.131.52 (talk) 19:52, 22 October 2013 (UTC)
Specifically the backwards 6s.220.127.116.11 (talk) 19:59, 22 October 2013 (UTC)
- For almost every equation the variables are specified, and there are links to the related articles like De Broglie relations and partial differential equations. Nevertheless, I agree there are some notational gaps (such as partial derivatives - reverse "6"), and will try to fill them in. M∧Ŝc2ħεИτlk 15:27, 23 October 2013 (UTC)
- Done. Please point out any specific equations which lack definitions of symbols. Thanks, M∧Ŝc2ħεИτlk 15:43, 23 October 2013 (UTC)
When it talks about time-reversal symmetry, shouldn't it be that psi(x, t) = psi*(x, -t) where it is the complex conjugate on the right? Gronteam (talk) 18:43, 14 November 2014 (UTC)
Axiomatic construction using time-evolution operator[edit]
I guess the article is missing the key concept of axiomatic derivation of the Schrodinger's equation using the time evolution operator. This is the most natural and modern approach to understanding the equation (although, most likely, not originally proposed by Schrodinger). The details can be found, for example, in "Modern Quantum Mechanics" by J. J. Sakurai or this lecture by Prof. Susskind. - Subh83 (talk | contribs) 22:07, 21 February 2014 (UTC)
Distance and potential confused in Constant Potential section[edit]
I was going to cut part of a sentence, but I decided to associate it with the following sentence so it'd flow right and not cause the misapprehension that made me thik of cutting it. 22.214.171.124 (talk) 17:54, 10 May 2014 (UTC)
- Actually, now that I've edited it, I think the text doesn't really go with the picture. It sounds like it's describing a particle in a box, not a particle impinging on a single wall. I'll think more and maybe improve on it later. If there's an equally good animation of the particle in a box, this paragraph could be used with it in a new section (maybe collapsed a bit since it's somewhat redundant). 126.96.36.199 (talk) 18:01, 10 May 2014 (UTC)
"Derived from symmetry principles"??[edit]
I never noticed this untill now. Someone in the lead has made the claim:
- "But Schrödinger's equation, although often presented as a postulate, can in fact be derived from symmetry principles."
with the citation to the book:
- Ballentine, Leslie (1998), Quantum Mechanics: A Modern Development, World Scientific Publishing Co., ISBN 9810241054</ref>:Chapter 3
So apparently the SE is not a postulate but can be "derived". Is this a misunderstanding of the editor who added the citation? Is the author of the book making a non-mainstream claim? Why would so many other sources treat the SE as a postulate while this random textbook says it can be derived?
I suggest removing it
, could be WP:OR. M∧Ŝc2ħεИτlk 10:12, 14 September 2014 (UTC)
- ...or at least rewriting it, saying that some authors say it is a postulate while others consider it to be derivable, and for the latter case what the foundations are to "derive" it from symmetry principles (most likely it is justified by symmetry principles, but I could be wrong). I may be very picky - but this is an important point to make clear about the equation. M∧Ŝc2ħεИτlk 21:41, 15 September 2014 (UTC)
- When one works backwards and takes the symmetries of an equation and adds the necessary constraints, you can derive almost anything. In this case the required symmetry is presumably Galilean relativity, and a constraint to a scalar field, conservation of energy and a perhaps a few others ... I don't think that it belongs in the lead. —Quondum 01:17, 16 September 2014 (UTC)
- In the lead we need to state at the outset whether or not the equation is a postulate or a derivable equation. These are two different things. There have been a number of confused edits to the article (and likely other QM articles) which assert the SE can be derived.
First I'll wait for more opinions before making changes.M∧Ŝc2ħεИτlk 20:46, 26 September 2014 (UTC)
- In the lead we need to state at the outset whether or not the equation is a postulate or a derivable equation. These are two different things. There have been a number of confused edits to the article (and likely other QM articles) which assert the SE can be derived.
- Well, actually I made the changes anyway, along my own proposal since no one has objected, but when possible input from others would still be very helpful. M∧Ŝc2ħεИτlk 23:47, 26 September 2014 (UTC)
"Simultaneous Positions"[edit]
Removed the metaphysical waffle of "...can be in several different locations at the same time...". That sort of description has no basis in standard quantum mechanics. Any experiment that can only be interpreted as a particle in two positions, would constitute an actual measurement of a particle having two eigenvalues at the same time. However, such a measurement would falsify a basic postulate of QM that requires all measurements to result in a single eigenvalue. The basic issue here is that QM is quantum, not classical. A classical argument might well result in such nonsense, but its not part of QM. — Preceding unsigned comment added by Kevin aylward (talk • contribs) 10:24, 30 August 2015 (UTC)
Again removed the line stating that states "...proves particle went through both slits at once." after my edit was reverted. It "proves" diddly squat. There are many interpretations of Quantum Mechanics that can "explain" such behavior without such an assumption, for example Bohmian Mechanics. Secondly, again, such an assumption contradicts QM, despite claims by otherwise qualified individuals to the contrary. The standard mathematical formulation of QM requires that the probability of a system exhibiting two simultaneous eigenvalues is zero. Period. There is no disagreement or controversy on this. Unfortunately, many "experts" appear to forget what a Hilbert space demands when they have their descriptive hat on rather than their mathematical one. Claims as to what values are before measurement are vacuous metaphysics and not part of, nor relevant to, the standard formalization of Quantum Mechanics. Kevin Aylward 15:14, 5 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
"Schrödinger Derivation"[edit]
Modified the claim that Ballentine presents arguments for the actual derivation of Schrödinger's equation. Ballentine references and reproduces other work that "derives" certain results that are usually derived from analysis of Quantum Mechanics. Symmetry arguments result in commutation relations such as [G, P]=ih (page 76). I see no argument presented in Ballentine for the actual derivation of the equation itself. It is simply postulated that a physical variable is represented by a Hermitian operator, a Hermitian operator necessarily satisfies A|psi>=a|psi>. It is simply postulated that the eigenvalues and vectors of the operator are the only possible physical values. It is simply postulated that |psi> gives the probability. Kevin Aylward 09:06, 5 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
- Thanks for clearing it up. It was most likely the misunderstanding of whoever added the claim. M∧Ŝc2ħεИτlk 11:38, 5 September 2015 (UTC)
- There is a lot more worse wrong with the whole article. I had one attempt to remove "proves particles takes two paths an once" but this was reverted. I don't have a lot of time to never ending correct all the blatant misconceptions. I am not sure the best way to tackle this comic book view of QM. So few understand that QM is a mathematical structure that predicts probabilistic results, and 99.9% of practitioners don't care a toss about waffle interpretations. All the waffle is a direct result of not accepting that QM is a new axiom of physics. It simply can not be explained by discussing which way some hypothetical entity may or may not travel. Classical reasoning always gets you contradictions, hence is false. Luboš Motl gets this bit spot on. I have a short wordy description here http://www.kevinaylward.co.uk/qm/quantum_mechanics.html, and reference Motl's page with the relevant math, although he is discussing a different problem. Kevin Aylward 14:31, 5 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
"Only One Wave Equation"[edit]
Added a Ballentine sourced quote that illustrates the fundamental issue with claiming that particles are really waves. It should be noted that there is absolutely no disagreement in standard quantum mechanics that there is only one wave equation for a multi particle system. For example, the Debroglie wavelength of a molecule is a single number, irrespective of the fact that may be several sub particles. This wavelength may be either much larger or much smaller than the size of the molecule. Quantum mechanics simply don't work by imagining little wave packets for each particle. dah...Kevin Aylward 08:23, 6 September 2015 (UTC)
r in the equations goes undefined[edit]
Noticed that r is not defined, I am making the assumption that r is the radius along the axis of wave propagation, but formally r should be defined. PB666 yap 12:22, 25 March 2016 (UTC)
Equation boxes[edit]
To me, the equation boxes in Schrödinger_equation#Equation seem redundant. I could see the value of an equation box to highlight the result if there is a derivation with several equations (as in Angular_momentum#Collection_of_particles), but here there is a subsection each for the time-dependent and time-independent versions, and both equations in each subsection are highlighted. Shall we remove the boxes? RockMagnetist(talk) 16:12, 12 April 2016 (UTC)
- Boxes are not limited to the results of a derivation, they make the main equation(s)/definition(s) of a subject stand out, titles are for reference.
- For this article, I don't mind if the boxes are kept, or deleted to reduce clutter and redundancy. If they are kept, it would be preferable to just use the minimalistic black/white theme, but people keep reinstating the blue/green colours.
- As a related aside, I have used them a lot in Lagrangian mechanics and Lorentz transformations with a minimalistic black/white theme, because those are equation-heavy articles (coloured boxes have been added by other editors), the titles are for self-contained reference if someone wanted to name the equation in a box. M∧Ŝc2ħεИτlk 21:10, 12 April 2016 (UTC)
- Yes, derivations are just the first example I thought of for equation-heavy articles or sections where the boxes might make sense. RockMagnetist(talk) 01:44, 13 April 2016 (UTC)
In Dublin in 1952 Erwin Schrödinger gave a lecture in which at on point he jocularly warned his audience that what he was about to say might "seem lunatic". It was that, when his equations seem to be describing several different histories, they are "not alternatives but all really happen simultaneously". This is the earliest known reference to the multiverse (David Deutsch, The Beginning of infinity, page 310). Kartasto (talk) 11:22, 16 April 2016 (UTC)
- Wikipedia articles that use American English
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- B-Class physics articles
- B-Class physics articles of Top-importance
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- WikiProject Chemistry articles
- Wikipedia pages with to-do lists


text:
The Sacramento Bee newspaper
- May 3, 2016
( 463)
Connect to the new Sacramento Bee Newspaper's Android app wherever you are.
• Breaking news alerts and real-time updates.
Receive the latest local and breaking news from Sacramento, Roseville, Elk Grove, Folsom, and El Dorado, California. The Sacramento Bee and SacBee.com reports on the local topics you care about including local, weather, traffic, crime, sports and national news.
Features of the app include:
• Breaking news alerts and real-time updates.
• The local news and sports topics you care about from around the Sacramento area.
• View stunning photos and galleries of news coverage and events.
• The Sacramento Bee opinions, editorials, and columns you love.
• Ability to share stories and galleries on Facebook, Twitter, or by email.
Easy access Love having easy access to latest news on my phone, sorted by news category. Quick scan and then click through for more detail if interested.
Keeping on top of what's happening Nice to carry the Bee app where ever you go for the latest breaking news ...
Hometown news I lived in Sacramento for many years and I love reading about the going ons there. I have been away for many years but my heart is still there.
Sacramento Bee. Love getting it online. Up to date news. Should be able to keep up with the RiverCats. Great article writing!.
Great local news app Necessary ads are unobtrusive, and navigation among different sections is easy. Use it as my main source for local news.
Like the news. Wish that the alerts link to the related article instead of going to the home page.
What's New
- Notification icons fixed
- Sharing Stories now shares the headline of the story
- Tapping phone numbers now properly takes user to phone
- Message Center bug fixed
Livestreaming, breaking news alerts, and the news that matters from FOX40 News

subset: commoncrawl


text:
I'm new to android development. I'm developing an application for android 4.0.3 devices, in my app I capture an image using camera.
When I test in the emulator (android 4.0.3), clicking the capture button displays the following message
your sd card is full. So please help me to solve the issues.


text:
On Friday 4th December 2015 the Mayfair unveiled HENNESSY Rooftop Bar… offering the height of city chic and elegance, and a place to feel special in the company of good people.
At level 13 of Adelaide's new 5 star Mayfair Hotel, HENNESSY will offer a rooftop bar experience like no other. Named after the building's original architects HENNESSY is available to both Mayfair Hotel guests and discerning visitors. Beautifully appointed and stylish interior space leads out to an open-air deck and balcony, where guests will enjoy stunning views of Adelaide.
Offering premium Champagne and house cocktails HENNESSY will offer guests a carefully crafted selection of high end wine, beer and spirits.In keeping with the style of the Mayfair guests may also select from a menu of classical bar snacks.
Mood and ambience will be carefully crafted with live music and DJ options at weekends. Entrance to the bar is via the Mayfair's lower level, Mayflower Lounge Bar.
Due to its location and offering HENNESSY is in high demand, enquiries for large group private functions on Sundays - Thursdays are welcome however a minimum spend requirement applies. For all booking enquiries please contact our sales team on +61 8 8210 8888 or email@example.com for enquiries.
Are looking for that perfect spot to have your wedding photos? HENNESSY is a stunning location to capture that special moment. Stay with us on your wedding night for the opportunity to have your photos taken in Hennessy on your wedding day.
Note: Smart dress code applies. Hotel Management reserves the right to refuse entry.
Hennessy's standard opening hours are as follows. Note: this is subject to change and may alter on public holidays, please call (08) 8210 8888 for further information.
- Monday – Thursday: 4pm to 11pm
- Friday: 3pm – 2am
- Saturday: 4pm – 2am
- Sunday: 2pm – 10pm
Special Opening Hours: Sunday 12 May - HENNESSY will remain open until 11pm
HENNESSY Closure Dates
HENNESSY will be closed on the following dates for private functions. Mayflower Bar on the lower level will be open for drinks during these times as an alternative.
- Sunday 7 August from 2-11pm
- Friday 29 July from 3pm - 2am
What's On
The South Australian Living Artists (SALA) Festival is the largest visual arts festival in Australia. The extensive visual .. Read More
Moon Lantern Festival 17 September 2016 This year's Moon Lantern Festival will be spectacular! Australia's l.. Read More
OzAsia Festival is Australia's leading international arts festival dedicated entirely to engagement with Asia. Adelaide F.. Read More


text:
Can anybody help me on "what all users are using the undo tablespace and how much" in oracle database 11g r2. any pointers would be much appreciated.
Database Administrators Stack Exchange is a question and answer site for database professionals who wish to improve their database skills and learn from others in the community. Join them; it only takes a minute:
Sign up
Sign up
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
This shows you the amount of undo size used by each session that is currently active.
Undo is not used by users directly but by statements which modify many database blocks. Try to search for session which generates a lot of redo.
Or for active transactions:
Or look at the view V$UNDOSTAT.


text:
Current and Upcoming Youth Sports:
The Los Alamitos Recreation & Community Services Department offers an array of sports to keep your child busy and active throughout the year.
Youth Volleyball
Begins week of September 12th, 2016
Pee Wee Soccer
Begins June 20th, 2016
Jr. Pee Wee Soccer
Begins June 28th, 2016
Pee Wee T-Ball
Begins July 26th, 2016
Jr. Pee Wee T-Ball
Begins July 27th, 2016
Jr. Pee Wee Flag Football
Begins September 13th, 2016
Jr. Pee Wee Basketball
Begins October 19th, 2016
For more information on how to register for these and any other programs,
please call (562) 430-1073.
Want to see pictures of our youth sports and receive regular updates on programs? Like us on Facebook! Simply search "Los Alamitos Recreation Youth Sports" or click on the Facebook icon above.


text:
Fleshlight play
- Runtime:
- 0:51
- Views:
- 3279
- Date:
- 3 years ago
- Rating:
- (15 votes) 100%
Fucking my fleshlight. Just a short video, no cumshot.
Very sexy, you look fantastic and your cock looks so hot smashing into that FL!
wish it was my ass
You are absolutely fucking hot. To see your big dick, your face and the FLESHLIGHT at the same time from this angle is absolutely mouthwatering and fucking masculine and manly, dude. I love to fuck my Fleshlight watching your video, doing the same.
Next time, play with my hole, please ! :p


text:
Man Vs Child
A witty, insightful romantic comedy, which draws on the author's experience of the comedy world, working in radio, and being immature and childless! For fans of David Nicholls, Ben Elton and Nick Hornby.
A witty, insightful romantic comedy, which draws on the author's experience of the comedy world, working in radio, and being immature and childless! For fans of David Nicholls, Ben Elton and Nick Hornby.
Dan McIntyre isn't ready to settle down. As a stand-up comedian with a career that's taking off, it was easy to walk away from his girlfriend's ultimatum: comedy or kids.
But now he's starting to feel like he's the last man standing while all his friends are switching socialising for baby wipes. Sure, his mates are still wide awake at 3am with a bottle in their hand – but now it's for a very different reason.
Dan reckons he spends enough time with spoiled brats in his day job wrangling a breakfast radio duo known as Bry Dynamite and Silly Sally. He can't understand why everyone's giving up their social lives for creatures who express themselves through loud, irritating noises and bodily fluids. But at least it's giving him material for a new comedy show, Man Vs Child.
Then Penny, the woman who broke his heart in high school, walks back into his life. She's newly single, and wants to reconnect with her old pal from French class – except now she has a one-year-old son...
Useful Links
10 Reader ReviewsSee All Reviews
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RussellVJWard4 stars
11 September 2013 at 10:23amReport
Dominic Knight, the comedy writer, broadcaster and The Chaser co-founder recently released his third book, Man Vs Child. It's a witty and amusing look at a single, thirty-something man's existence in Sydney as he watches those around him embrace a life of screaming babies, dirty nappies and ever-present baby wipes, leaving him as the last man standing. The books draws on Dom's experience of the comedy world, working in radio, and being immature and childless, and the insights into his 'real' life are apparent throughout the book. The lead character, Dan, spends his day with highly-annoying breakfast radio, Bry Dynamite and Silly Sally, and his nights as a budding stand-up comedian, but can't understand why anyone would want to spend their free time dealing with children. That is, until his childhood sweetheart, newly single Penny, walks back into his life... with her young son. If you're a fan of David Nicholls, Ben Elton and Nick Hornby, you'll enjoy Dom's latest book, which ranges from laugh-out loud moments in the radio station and on the stage to those poignant times when it becomes obvious that Dan is being left behind and needs to catch-up fast. Sometimes books in the spirit of Man Vs Child try too hard to elicit a laugh at the expense of others less fortunate but Dom treats the story with sensitivity and humour. You get a true, real-life sense of Dan's emotional struggles with his friends, girlfriends and current way of life.
JarrahJungle4 stars
5 September 2013 at 11:33amReport
This is an autobiography of Dominic Knight an Australian guy in his early 30s, who works at a radio station by day and follows his passion for stand up comedy by night. As Dom's friends pair up and start families he finds himself surrounded by couples with snotty nose kids and a totally different lifestyle which leads him into writing material for his Man Vs Child comedy skits. The story continually goes back to the internal debate of whether Dom wants to have kids, grow up, and stop being a kid himself. Dom runs into his high school sweetheart Penny who has a 1 year old son and the more time Dom spends with them the more he realises the whole kid thing isn't so bad after all. The novel is written in a very simple and easy to follow style, the characters were described well and Dom was like listening to a mate tell me funny stories or run down on conversations and things that happened, it was a very relaxed read. True to Dom's comedy background the novel was funny, witty, and very cheeky. I recommend this book to young Australians who would like to know a bit about Sydney's radio and comedy scene. I would also recommend it to men (and women) who are unsure if they want to start a family, it gives some great points from both sides of the fence but in a laid back approach so you don't feel like you're getting a lecture.
MrsMichelleS4 stars
30 August 2013 at 11:13amReport
This was a great comical read. It was light and refreshing and had quite a few laugh out loud moments. The story also had gravity and weight about it, with real issues and thoughts and feelings. I sincerely hope that I haven't bored my single childless friends with my 'kid' stories like Dan's friends did to him! He was spot on with his child humour and I giggled many times. The romance was an excellent love story about the one that got away, the one that could have been, our first crush…. This was a tremendous read, it had a great balance of fun and humour and depth and story. I loved the radio storyline and it made me wonder who Bry and Sally may have been! Any hints Dominic? Definitely recommended!
Sam Still Reading5 stars
11 August 2013 at 9:03pmReport
I finished this book just a few hours ago and ever since, it's been going through my mind. There are several awesome things about Man Vs Child, the first being Dan's stand up. It reads as really funny, actually making me laugh out loud. I don't usually get that with written funny stuff.The second is commercial breakfast radio – thanks to Dom Knight, I can never listen to it again with thinking some cynical thoughts. Another thing I loved was Dan. He is a lovely character – realistic, slightly geeky yet rather delightful. I have a bit of a fictional crush on him. Knight reveals all sides to Dan's character, from the good to bad. He's so honest and the thoughts he reveals are not something you'd usually read from an Australian bloke. I don't want to give away the plot, but wow, some of it is a complete rollercoaster. In the last hour of reading, I went from happy to sad, and then finally astonished. The ending is magnificent – I didn't know how to feel. Should I be happy? Sad? Worried? It's a realistic ending and original. Dom Knight is my generation's Nick Earls and Nick Hornby. He writes books from a male perspective that have humour, heartbreak and wisdom. I love it. More please! A 10 out of 10 read (and I don't give those away lightly). (If anyone decides to name their child Elspeth after reading this book; I think you've completely missed the point!)
Melissa3173 stars
4 August 2013 at 8:06pmReport
Dominic Knight, best known for The Chaser and an ABC radio host, has developed something of a side career as the voice of clucky single men. He's turned these musings into a novel, Man vs Child, the story of Dan, a single 34 year-old Sydney man with a well-paying job in the squalid world of FM radio, who plays to unappreciative audiences as a comedian. Dan's world is shrinking as his friends pair off, breed, and move to the suburbs. His social life revolves around toddler birthday parties and nap time. He is terrified of being sucked into the life-ruining vacuum of parenthood, but an old flame shows up, a newly single mum, and he discovers the pull of tiny humans. I'm not sure men get the same hurry up and breed message women do, but Dan is feeling the pressure to conform to parenthood just the same. There's a list of boxes you're supposed to tick when you're a good, middle-class boy, but Dan doesn't buy into the idea that his life is less meaningful for lack of offspring. Nonetheless, he got the degree, the job and the the property. And with Penny and Lloyd (the baby names in this novel are spot on) in his life, he starts to understand the appeal. It's not all babies. Knight gets stuck into commercial radio and the odious men who populate it and the stand-up comedy scene. He writes with a light touch and an engaging style that makes for an easy read.
About the authorMore
Dominic Knight
Dominic Knight is the Evenings presenter on 702 ABC Sydney and ABC Local Radio NSW/ACT. He has worked on The Chaser's creative projects in media, including print, online, stage, radio, television and karaoke videos. He wrote his novels - Disco Boy, Comrades and Man Vs Child - largely because he enjoys boasting at dinner parties that he is a novelist.
Dominic Knight BooksMore
- Comrades
by Dominic Knight
Romeo and Juliet amidst university campus politics.
- Disco Boy
by Dominic Knight
A hilarious novel from a great comedic writer, one of the founders of The Chaser's War on...
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'Excellent... Harrowing, humane and brilliant.' - The Times (UK)
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text:
Change to VHIEP will reduce feesJanuary 30,2014Change to VHIEP
will reduce fees
Families that use the states 529 college savings plan will soon be able to save just a little bit more.
The 14,000 account holders with the Vermont Higher Education Investment Plan (VHIEP) will see a reduction in the amount of fees they have to pay under the program. The change is projected to save account holders approximately $100,000 annually.
Nearly every state offers some sort of 529 college savings plan, which is named after the provision in the IRS tax code that allows states to offer tax incentives to save for college. Vermont provides a nonrefundable tax credit of 10 percent of the first $2,500 contributed per beneficiary, per year.
VHIEP, which began in 1999, has $225 million in assets. To date, 3,470 students have used more than $78 million from VHEIP accounts to pay for education or training after high school.
In 2012, $36 million was invested into VHEIP, with about $1.8 million realized in tax credits.
VHEIP accounts can be started with as little as $25. For more information, visit www.vheip.org or call (800) 637-5860.MORE IN This Just In
Police say a too-quick reaction to a GPS system's directions sent a Toyota Corolla... Full Story To our readers: This morning we had an issue that has prevented timely delivery of... Full Story
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text:
|By Marketwired .
Article Rating:
|March 27, 2014 08:07 PM EDT
VANCOUVER, BRITISH COLUMBIA -- (Marketwired) -- 03/27/14 -- GVIC Communications Corp. (TSX: GCT) ("GVIC" or the "Company") reported cash flow, earnings and revenue for the year ended December 31, 2013.
Summary Results
Results are reported below on an adjusted basis to include the Company's share of the results of its joint ventures. Management bases its operating decisions and performance evaluation utilizing these results. Refer to Impact of Joint Venture Accounting on page 5 for discussion of the accounting change and results in accordance with IFRS.
---------------------------------------------------------------------------- (thousands of dollars) except share and per share amounts 2013 (5) 2012 (5) 2011 (5) ---------------------------------------------------------------------------- Revenue $ 328,898 $ 330,016 $ 267,394 EBITDA (1) $ 43,714 $ 51,010 $ 49,744 EBITDA margin (1) 13.3% 15.5% 18.6% EBITDA per share (1) $ 0.146 $ 0.170 $ 0.166 Net income attributable to common shareholders before non-recurring items (1)(2)(3) $ 17,295 $ 17,551 $ 25,380 Net income attributable to common shareholders per share before non-recurring items (1)(2)(3) $ 0.058 $ 0.058 $ 0.084 Cash flow from operations (1)(2)(3) $ 43,156 $ 50,814 $ 43,048 Cash flow from operations per share (1)(2)(3) $ 0.144 $ 0.169 $ 0.143 Debt net of cash outstanding before deferred financing charges $ 126,771 $ 144,523 $ 152,819 Dividends paid (4) $ 5,408 $ 5,477 $ 2,704 Dividends paid per share (4) $ 0.018 $ 0.018 $ 0.009 Weighted average shares outstanding, net 300,425,031 300,425,031 300,425,031 ----------------------------------------------------------------------------
1. Refer to "Non-IFRS Measures" section of the financial statements. 2. 2013 excludes $5.7 million of restructuring expense and $1.3 million of transaction and transition costs, 3. $79.0 million of impairment expense, $0.2 million gain on acquistion, and $0.4 million net gain on disposal of assets. 4. For non-recurring items excluded in the prior period, refer to previously reported financial statements. 5. Dividends in 2013 total $0.024 per share paid quarterly, dividends in 2012 total $0.018 per share paid semi-annually, quarterly dividends totalling $1.8 million or $0.006 per share were declared in November 2013 and paid on January 3, 2014. 6. These results are presented on an adjusted basis to include the Company's share of the results of its joint ventures, as management bases its operating decisions and performance evaluation on the adjusted results.
Key Financial Highlights (1)
-- Same-store consolidated revenue was up 1.2% for the quarter ending December 31, 2013 and consolidated earnings before interest, taxes, depreciation and amortization (EBITDA) was up 16.1% for the same quarter compared to last year on an adjusted basis; -- For the year ended December 31, 2013, GVIC's adjusted consolidated revenues decreased 0.3% or $1.1 million to $328.9 million from $330.0 million the prior year; -- For the year ended December 31, 2013, adjusted consolidated EBITDA declined 14.3% to $43.7 million from $51.0 million the prior year. EBITDA was affected by $2.0 million in one-time accounting and other expense items, as well as $1.9 million of operating cost investments made in agriculture digital and data, the launch of the Company's environmental risk information business into the U.S. and REW.ca real estate information development initiatives. Excluding these amounts, consolidated adjusted EBITDA was $47.7 million, off 6.6% from the prior year; -- Adjusted cash flow from operations (before changes in non-cash operating accounts and non-recurring items) decreased 15.1% from the prior year to $43.2 million; -- Adjusted net income attributable to common shareholders before non- recurring items was $17.3 million, compared to $17.6 million the prior year; -- Adjusted EBITDA per share decreased 14.3% to $0.146 per share from $0.170 per share for the year compared to the prior year and net income attributable to common shareholders before non-recurring items per share was consistent with the prior year at $0.058 per share; -- Adjusted cash flow from operations (before changes in non-cash operating accounts and non-recurring items) decreased to $0.144 per share from $0.169 per share for last year; -- The Company (excluding its joint ventures) reduced debt by $23.3 million during the year, of which $12.0 million was generated by the sale of real estate assets; and -- As a result of the continued structural changes in the print media industry resulting from digital competition and weaker economic conditions, and reduced valuations for print newspaper assets, the Company recorded an impairment of its goodwill, intangible assets and investment in associate of $79.0 million, primarily in its community media assets.
(1) These results are presented on a proportionate consolidation basis, and include the Company's shares of revenue, expenses, assets and liabilities from its joint venture operations, which reflects the basis on which management makes its operating decisions and performance evaluation. Refer to the Impact of Joint Venture Accounting, below, for impact of proportionate consolidation accounting and the Company's results in accordance with IFRS.
Review of Operations and Value Enhancement Initiatives
GVIC Communications Corp. completed 2013 with a stronger fourth quarter, in which same-store consolidated revenue increased 1.2% and consolidated EBITDA was up 16.1% for the quarter compared to last year on an adjusted basis(1).
Notwithstanding a $79.0 million accounting charge taken for impairment of goodwill, intangible assets and investment in associate relating primarily to a reduction in the carrying value of community media assets, which resulted in a significant reduction in net income for 2013, the fourth quarter results were very encouraging and represented a significant improvement in business and operating results compared to the softness experienced earlier in the year. Significant reduction in debt and improved strength in operating position was also achieved during the year through principal repayments made from operating cash flows and the sale of real estate and non-core assets. Management intends to continue to use free cash flow to further reduce debt and pay dividends to shareholders, amongst other things.
Improved operating performance resulted from both new revenue initiatives that generated higher sales, complemented by significant cost reductions implemented throughout the year. Through this process, the Company executed against a comprehensive strategy to Evolve, Enrich and Extend its information products and services. In 2013, new digital and data tools and services were launched, which contributed to higher sales and profitability within key business information verticals.
For the year ended December 31, 2013, consolidated revenue decreased 0.3% to $328.9 million and consolidated EBITDA declined 14.3% to $43.7 million compared to last year on an adjusted basis(1), primarily due to weaker community media revenues, which were impacted by overall economic conditions in 2013 and digital competition. These were offset by stronger business information revenues. The variance in EBITDA was also the result of approximately $2.0 million of one-time non-cash expenses and changes in deferred revenue accounting, as well as $1.9 million of operating cost development investments made in agriculture digital and data, the launch of the Company's environmental risk information business into the U.S. and REW.ca real estate information development initiatives. New revenues began to be realized from these investments in the fourth quarter of 2013 and the first quarter of 2014.
Excluding the $3.9 million of one-time non-cash expenses, accounting changes and development investments, adjusted(1) consolidated EBITDA for the year ending 2013 was $47.7 million, which was only 6.6% off of 2012 consolidated EBITDA of $51.0 million, despite the economic and other challenges faced in 2013.
Business Information
Many of the Company's business information operations (which include business and professional and trade information) continue to grow and provide attractive opportunities for future growth. In particular, the energy, agriculture, environmental services, financial services, manufacturing and construction verticals performed well. Management is investing in these verticals to develop rich information tools and services, including new environmental risk, weather and farm management and upstream oil and gas platforms. Management is also reviewing the spectrum of verticals in which it operates with a view of focusing resources on those verticals with high growth and strong positions.
Business information operations now represent more than half of GVIC's EBITDA. Further, 45% of the business information EBITDA comes from rich information digital data products designed for scalable growth and higher profitability. Many product lines offer resiliency in challenging economic times as they provide critical insight and analysis to GVIC's customers.
GVIC's business information portfolio contains many brands that have decades of service in their respective sectors. The intrinsic equity associated with these brands is a key competitive advantage as the Company pursues its Evolve, Enrich and Extend strategy. Consistent with this strategy, management is focused on initiatives designed to offer customers increasingly richer value propositions. These include multi-platform solutions designed to integrate more seamlessly with customer decision-making processes, thus ensuring heightened levels of decision dependency. Digital revenues now represent more than one quarter of GVIC's business information revenues.
In 2013, a variety of initiatives highlighted how sharper focus on sector and customer needs is facilitating successful development and growth. They include:
-- Environmental Risk Information Service ("ERIS") expanded its business into the United States; -- WeatherFarm was re-engineered and re-launched to integrate new tools and data sets that augment the meteorological information and analytics of the Company's new Weather INnovations Consulting LP business, through which real-time weather data and intelligence is supplied to Canadian farmers and agribusiness companies; -- FarmMedia (the new DBA for GVIC's agricultural group) contracted with the Alberta Wheat Commission to provide syndicated market information to commission members through its website; -- Canada's Outdoor Farm Show ("COFS") achieved record results with its 20thAnniversary exposition. Nearly 43,000 delegates attended the show, which included more than 750 exhibitors.
Community Media
GVIC's community media operations offer broad coverage across Western Canada in local markets, and continue to offer a strong value proposition through local information and marketing channel utility.
As mentioned, generally weak economic conditions as well as structural changes in the community newspaper industry adversely affected advertising revenues during 2013. This impact has been particularly true of community operations in urban markets, such as the Lower Mainland of British Columbia, where both print and digital competition is stronger. Many of the Company's smaller rural community media markets - largely spread across the Prairies - have enjoyed more steady performance due to their strong local positions and local advertising revenues.
The media industry, as a whole, continues to pursue new "business models" intended to manage the future value of content against a backdrop of maturing traditional advertising and greater digital opportunities. GVIC is well advanced in this respect. Significant efforts are being made to develop new community media related special content and advertising focused products that are delivered in multiple platform formats.
While print advertising revenues were weaker in 2013, digital revenues continued to grow in GVIC's community media operations. Significant progress was made launching new digital offerings, with a focus on products that can be quickly monetized. Management is focused on bottom line growth from digital investments, rather than pursuing larger digital revenues without a positive contribution - a trend among many digital media companies. GVIC's community media digital revenues generated strong year-over-year growth in 2013, with an EBITDA margin that exceeded the group's print margin.
While economic and market challenges have affected the community media operations, management believes that these businesses remain strong and will continue to generate solid cash flow given the nature of the markets in which GVIC operates - particularly within the more robust micro-economies of Western Canada. This cash flow can be used to fund growth through both internal investment and acquisition of digital business information and community media assets, as well as debt repayments.
Financial Position
In 2013, the Company pursued initiatives to improve its financial position including:
-- Cost reduction initiatives. Given the softness experienced in the Company's community media operations, a variety of significant cost reduction measures have and are being implemented to reduce overall operating costs. The initiatives are targeted to reduce costs by more than $7.0 million on an annualized basis. Savings from these initiatives began to be realized in both the third and fourth quarters of 2013. In implementing these initiatives, management has been diligent to maintain the operating integrity of the businesses. -- Sale of real estate assets. The Company realized cash proceeds of $12.0 million on the sale of real estate assets in 2013. -- Subsequent to year end, the Company entered into an agreement to sell its real estate property in Kamloops for $4.8 million. The sale is expected to close in the summer of 2014. -- Other property dispositions are currently being negotiated. Given current capitalization and interest rates, monetizing real estate value to reduce leverage has been deemed prudent. The real estate sales have been targeted to a) cover any required deposit relating to the previously reported notice of possible reassessment from Canada Revenue Agency (CRA) for the 2008-2011 income tax years, should a deposit become payable and b) result in a net reduction of leverage from current levels. Any potential CRA reassessment timing is not currently determinable. -- Sale of non-core assets. During the fourth quarter of 2013, the Company sold two money-losing community newspapers and acquired several more profitable community media assets that provide a better strategic fit.
On an adjusted basis to include the Company's share of its joint ventures, GVIC's consolidated debt net of cash outstanding before deferred financing charges and other expenses was reduced to 2.90x trailing 12 months EBITDA as at December 31, 2013.
The Company (excluding its joint ventures) reduced debt by $23.3 million during the year (as stated above, $12.0 million was generated from the sale of real estate assets). GVIC's consolidated debt net of cash outstanding before deferred financing charges was $113.9 million as at December 31, 2013.
Capital expenditures were $11.7 million for the year ended December 31, 2013 compared to $7.1 million in the prior year. $10.1 million of these capital expenditures were investment capital expenditures, the majority of which relate to building, building improvements, new printing equipment, new office space and software. These investment capital expenditures are expected to result in attractive direct revenues and cash flow improvements, including lower operating costs and payback consistent with GVIC's targeted return on investment. Sustaining capital expenditures for the year were $1.6 million.
Management expects the level of investment capital expenditure in 2014 to be significantly reduced, with primarily only ongoing sustaining capital investments being required.
As a result of the continued structural changes in the print media industry resulting from digital competition and weaker economic conditions, and reduced valuations for print newspaper assets, the Company recorded an impairment of its goodwill, intangible assets and investment in associate of $79.0 million, primarily in its community media assets.
Declaration of Dividend
The Board of Directors declared a quarterly dividend of $0.006 per share to shareholders of record on March 25, 2014 and payable on April 7, 2014. The dividend is consistent with the Company's dividend policy of paying $0.024 per share per annum payable quarterly.
Impact of Joint Venture Accounting
As a result of a change in IFRS accounting policies effective January 1, 2013, the Company is now required to account for its joint venture operations under the equity method. Previously, the Company's joint venture operations were accounted for using proportionate consolidation. As a result of the change in accounting, the Company no longer includes the revenues, expenses, assets and liabilities of its share of these operations in the Company's results. The Company now carries its interest as a net investment on its balance sheet and includes the net results from these operations in its statement of operations.
Despite this accounting change, management believes that including its share of revenues and expenses in the Company's results (consistent with its prior accounting treatment) provides an important basis for assessing the overall operations of the Company. The table below adjusts the Company's reported results under IFRS to include the revenues and expenses of its joint venture operations, consistent with its historical presentation. Management continues to base its operating decisions and performance evaluation on the adjusted results.
---------------------------------------------------------------------------- (thousands of dollars) Year ended December 31, 2013 (4) except share and per share amounts Per IFRS Adjustment (4) Adjusted ---------------------------------------------------------------------------- Revenue $ 295,623 $ 33,275 $ 328,898 EBITDA (1) $ 33,467 $ 10,247 $ 43,714 EBITDA margin (1) 11.3% 13.3% EBITDA per share (1) $ 0.111 $ 0.146 Net income attributable to common shareholders before non-recurring items (1)(2)(3) $ 15,706 $ 1,589 $ 17,295 Net income attributable to common shareholders per share (1)(2)(3) before non-recurring items (1)(2)(3) $ 0.052 $ 0.058 Cash flow from operations (1)(2)(3) $ 34,495 $ 8,661 $ 43,156 Cash flow from operations per share (1)(2)(3) $ 0.115 $ 0.144 Debt net of cash outstanding before deferred financing charges $ 113,893 $ 12,878 $ 126,771 Weighted average shares outstanding, net 300,425,031 300,425,031 ---------------------------------------------------------------------------- --------------------------------------------------------------------------- (thousands of dollars) Year ended December 31, 2012 (4) except share and per share amounts Per IFRS Adjustment (4) Adjusted --------------------------------------------------------------------------- Revenue $ 297,111 $ 32,905 $ 330,016 EBITDA (1) $ 40,046 $ 10,964 $ 51,010 EBITDA margin (1) 13.5% 15.5% EBITDA per share (1) $ 0.133 $ 0.170 Net income attributable to common shareholders before non-recurring items (1)(2)(3) $ 16,395 $ 1,156 $ 17,551 Net income attributable to common shareholders per share (1)(2)(3) before non-recurring items (1)(2)(3) $ 0.055 $ 0.058 Cash flow from operations (1)(2)(3) $ 40,504 $ 10,310 $ 50,814 Cash flow from operations per share (1)(2)(3) $ 0.135 $ 0.169 Debt net of cash outstanding before deferred financing charges $ 137,167 $ 7,356 $ 144,523 Weighted average shares outstanding, net 300,425,031 300,425,031 ---------------------------------------------------------------------------
1. Refer to "Non-IFRS Measures" section for calculation of non-IFRS measures used in this table. 2. 2013 excludes $5.7 million of restructuring expense, $1.3 million of transaction and transition costs, $79.0 million of impairment expense, $0.2 million gain on acquistion and $0.4 million net gain on disposal of assets. 3. For non-recurring items excluded in the prior period, refer to previously reported financial statements. 4. Adjustment to include the Company's share of revenues, expenses and cash flows from its joint venture operations consistent with the Company's treatment on a historical basis and prior to implementing the new accounting standards.
Under IFRS, revenues for the year ended December 31, 2013 decreased 0.5% to $295.6 million from $297.1 million for the year prior. Cash flow from operations (before changes in non-cash operating accounts and non-recurring items) decreased 14.8% to $34.5 million and earnings before interest, taxes, depreciation and amortization (EBITDA) decreased 16.4% to $33.5 million compared to the year prior. Net income attributable to common shareholders (before non-recurring items) decreased by $0.7 million to $15.7 million.
Cash flow from operations (before changes in non-cash operating accounts and non-recurring items) for the year ended December 31, 2013 decreased to $0.115 per share from $0.135 per share for the same period prior year. EBITDA decreased to $0.111 per share from $0.133 per share and net income attributable to common shareholders (before non-recurring items) per share decreased to $0.052 per share from $0.055 per share.
The Company continues to grow its business information operations through its Evolve, Enrich and Extend strategy, which focuses on providing richer content, data and information, related analytics and business and market intelligence in order to achieve greater customer utility and decision dependence. The strategy is also being used to improve the community media operations. Management expects growth will continue in GVIC's business information operations, as well as community media markets where local market conditions are stronger and digital competition is relatively weaker.
While media maturation factors are having an impact as described, the softer economy is playing a significant role in dampening revenues, and economic strengthening should result in improved revenues at the margin. Management will continue to closely monitor economic conditions in various markets and verticals to ensure long-term viability.
Management will focus in the short-term on a balance of paying down debt, reducing costs and improving profitability, enhancing existing operations, targeting select acquisition opportunities and returning value to shareholders through growth in cash flow per share and payment of dividends.
As indicated, significant focus and related investment will continue to be made to enhance GVIC's business information verticals, through both organic development and acquisition. These acquisitions will be targeted to expand markets that GVIC covers, expand the breadth of information products and marketing solutions, and expand GVIC's digital media staff, technology and related resources.
Once leverage is reduced to more moderate levels, management will seek an ongoing balance of maintaining debt at those levels and delivering increased value to shareholders through both operations and acquisitions, as well as dividends.
Shares in GVIC are traded on the Toronto Stock Exchange under the symbol GCT.
About the Company: GVIC Communications Corp. is an information communications company focused on the provision of primary and essential information and related services through print, electronic and online media. GVIC is pursuing this strategy through its core businesses: the community media, trade information and business and professional information markets.
Financial Measures
To supplement the consolidated financial statements presented in accordance with International Financial Reporting Standards (IFRS), GVIC uses certain non-IFRS measures that may be different from the performance measures used by other companies. These non-IFRS measures include cash flow from operations (before changes in non-cash operating accounts and non-recurring items), net income attributable to common shareholders before non-recurring items and earnings before interest, taxes, depreciation and amortization (EBITDA), which are not alternatives to IFRS financial measures. Management focuses on operating cash flow per share as the primary measure of operating profitability, free cash flow and value. EBITDA per share is also an important measure as the Company has low ongoing capital expenditures and depreciation and amortization largely relates to acquisition goodwill and copyrights and does not represent a corresponding sustaining capital expense. These non-IFRS measures do not have any standardized meanings prescribed by IFRS and accordingly they are unlikely to be comparable to similar measures presented by other issuers.
Forward-Looking Statements
This news release contains forward-looking statements that relate to, among other things, the Company's objectives, goals, strategies, intentions, plans, beliefs, expectations and estimates. These forward-looking statements include, among other things, statements relating to the Company's expectations regarding revenues, expenses, cash flows and future profitability and the effect of GVIC's strategic initiatives, including its expectations to grow its business information operations, to implement cost reduction measures, to sell real estate properties and utilize proceeds of such sales to cover required CRA re-assessment deposits, to produce products and services that provide growth opportunities, to organic development and new business acquisitions, to improve profitability, to grow cash flow per share, to pay dividends and to reduce debt levels and as to its expectations as to the level of investment in capital expenditures. These forward-looking statements are based on certain assumptions, including continued economic growth and recovery and the realization of cost savings in a timely manner and in the expected amounts, and are subject to risks, uncertainties and other factors which may cause results, performance or achievements of the Company to be materially different from any future results, performance or achievements expressed or implied by such forward-looking statements, and undue reliance should not be placed on such statements.
Important factors that could cause actual results to differ materially from these expectations include failure to implement or achieve the intended results from GVIC's strategic initiatives, the failure to implement or realize cost savings in a timely manner or in the expected amounts, the failure to negotiate or complete the sale of real estate assets, the failure to identify, negotiate and complete the acquisition of new businesses, the failure to develop new products, and the other risk factors listed in the Company's Annual Information Form under the heading "Risk Factors" and in the Company's MD&A under the heading "Business Environment and Risks", many of which are out of the Company's control. These other risk factors include, but are not limited to, the ability of the Company to sell advertising and subscriptions related to its publications, foreign exchange rate fluctuations, the seasonal and cyclical nature of the agricultural industry, discontinuation of the Department of Canadian Heritage's Canada Periodical Fund's Aid to Publishers, general market conditions in both Canada and the United States, changes in the prices of purchased supplies including newsprint, the effects of competition in the Company's markets, dependence on key personnel, integration of newly acquired businesses, technological changes, tax risk and financing and debt service risk.
The forward-looking statements made in this news release relate only to events or information as of the date on which the statements are made. Except as required by law, the Company undertakes no obligation to update or revise publicly any forward-looking statements, whether as a result of new information, future events or otherwise, after the date on which the statements are made or to reflect the occurrence of unanticipated events.
GVIC Communications Corp.
Mr. Orest Smysnuik
Chief Financial Officer
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Marvel Assembles an Official Title for Third "Avengers" Movie
Comic Books, Film
Showing results 1-40 of 1341
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