Say we have a particle in an infinite deep well that is $V(x)=\left\{\begin{array}{ll}0 &amp; 0 \leq x \leq L \\ \infty &amp; \text { elsewhere }\end{array}\right.$. The energies corresponding to various states are given as $E_n=\frac{n^{2} \pi^{2} \hbar^{2}}{2 m L^{2}}$.This means that the particle can have different energies upon different measurements. But this goes against the rule that the total energy of a system remains constant,because if I measure the energy now it's something and later on it may be something else, violating conservation of energy! Where am I wrong?
Consider a particle in a potential well. Let’s assume it’s a simple harmonic oscillator potential and the particle is in its ground state with energy E0 = (1/2) &#8463;&omega;0. We measure its position (measurement-1) with a high degree of accuracy which localises the particle, corresponding to a superposition of momentum (and therefore energy) states.  Now we measure the particle’s energy (measurement-2) and happen to find that it’s E10 = (21/2) &#8463;&omega;0. Where did the extra energy come from?  In the textbooks it’s claimed that the extra energy comes from the act of observation but I wonder how that could work. Measurement-1 which probed the position of the particle can’t have delivered to it a precise amount of energy, while measurement-2 might just have been passive. No doubt there is entanglement here between the particle state and the measuring device but where, and which measurement?
Why are my sprinkles beneath the frosting I am a beginner to Blender and watching .  At 8:46 is when my problem occurs, because my sprinkles are appearing beneath the icing. For PhD applications, I have mentioned that I am interested in some research areas. Besides, I am thinking about mentioning some professors' names, so that it shows I have read their websites and I am not just sending out generic statements applicable to many schools.  But is it good to mention some professors' names in the statement of purpose, if I don't know them personally? In what cases is it good, and in what cases it isn't?  For example, is it good to only mention    those whose research directions are aligned with my research interests, or/and those whose books or notes I have heard of, or better, might have read some parts of, or/and those who are already established and famous (such as having certain titles), or/and those that are directing the PhD graduate programs, or/and those that are heads of the departments?    What will other professors who are not mentioned think? How will you do, if it were you? Difference between "I have got" and "I have gotten" I see these two expressions are used almost identically in different contexts. Is there a difference between I have got and I have gotten? Given a method signature:  public bool AreTheSame&lt;T&gt;(Expression&lt;Func&lt;T, object&gt;&gt; exp1, Expression&lt;Func&lt;T, object&gt;&gt; exp2)   What would be the most efficient way to say if the two expressions are the same? This only needs to work for simple expressions, by this I mean all that would be "supported" would be simple MemberExpressions, eg c => c.ID.  An example call might be:  AreTheSame&lt;User&gt;(u1 =&gt; u1.ID, u2 =&gt; u2.ID); --&gt; would return true What are the system requirements for each flavour of Ubuntu Desktop? I'm thinking about installing Ubuntu Desktop, but I don't know what flavor is the best for my system. What are the minimum and recommended hardware requirements? What kind of CPU? How much memory? Should I have Hardware Acceleration? What flavor should I use?  This is an attempt of a canonical answer. My answers have the &quot;official  requirements&quot;, the recommended are a mix of official sources and opinion based (along with the answer it's told the source). You can comment or edit if you feel that the information is obsolete or incomplete. It is a good rule of thumb that any system capable of running Windows Vista, 7, 8, x86 (Intel) OS X will almost always be a lot faster with any Ubuntu flavor even if they are lower-spec than described below. ORA-00918: column ambiguously defined in SELECT * Where can I ask questions about the computer problems I have been facing?  Current problems I am facing with my computers:   Windows 7 errors random "Blue screens of Death" computer randomly freezing up Xfire challenges Some faces of a model don't respond to UV Mapping I can't seem to get these particular faces to take the UV Mapping. I selected the entire object, entered edit mode, hit U>Unwrap.   The rest of the mesh takes the uv wrapping, but not those faces for some reason.    It looks normal in solid mode.     Does anyone know what could be causing this? Compton scattering vs. photoelectric effect Say a photon hits some atom.  What determines whether there will be a photoelectric effect (photon is absorbed, electron is released) or whether there will be a Compton scattering (the photon is  scattered at some angle, and the electron is released with another direction)? How can I change an element's class with JavaScript? I read some articles, and seen some videos about a github project that do a sort of thing, but it's a little bit outdated things.I wanna see if this thing is possible to do, nowadays. Thanks How can I move an installed game from one Steam library folder to another? I use (and have it much bigger) drive D: to store all my user data and games, but I have installed the Steam client on drive C:. When I was installing a first game (Warhammer 40000), I've chosen to place my library folder on drive D: and the game went there.  But now as I've got installed the second game (Portal), I can see that it was put on drive C: despite to the choice I've done previously. When I open Steam - Settings - Downloads + Cloud - Steam library folders, I can see both installation places in the list. Can I merge them into one?  I would even agree to use the default drive C: library (as I've replaced it with a symlink already). When I press to remove one library it says it can only remove empty ones. Evaluate $\int \frac{1}{(x^2+1)^2}dx$ $$\int \frac{1}{(x^2+1)^2}\mathrm dx$$ Look simple, but I stuck a little bit. What method is better in this situation? Please, help. How to learn physics effectively and efficiently I've been exploring implementing Angular 2.0 in Salesforce custom pages and found that if I set showHeader=true in the VF page, I run into some issues.   It looks like including the header loads "sfdc/main.js", which defines the browser's Map() function without checking if one already exists. This removes some needed prototype functions that are native to ES5/6 such as "set" (needed in Angular 2) and "delete" (needed for an ES6-shim).   I've found that even including an ES5 shim before the ES6 one in attempts to restore some of these prototype methods does not work. If I set showHeader=false, "sfdc/main.js" is not loaded and everything works fine.   Is there a recommended way around this, or is it possible to update "sfdc/main.js" to conditionally define Map() if one does not already exist? It looks like it leaves out quite a few native functions supported in modern browsers.  Thanks In RSA, why is it important to choose e so that it is coprime to φ(n)? When choosing the public exponent e, it is stressed that $e$ must be coprime to $\phi(n)$, i.e. $\gcd(\phi(n), e) = 1$.   I know that a common choice is to have $e = 3$ (which requires a good padding scheme) or $e=65537$, which is slower but safer.  I also know that for two primes $p,q$, we have $\phi(pq) = (p - 1) (q - 1)$  Now, let me give a (simple) example:  Say I choose $e = 3$, and two random primes $p = 5$ and $q = 13$.  I can now compute $\gcd(3, \phi(5 \cdot 13)) = 3$.  This reveals that $3$ and $\phi(n)$ are not coprime. I assume this could also happen for large values of $p$ and $q$, and likewise for another $e$. I therefore assume that the RSA algorithm must check that $\gcd(e, \phi(pq)) = 1$. But let's assume it doesn't.  How does RSA become vulnerable if $\gcd(e, \phi(pq)) \neq 1$? TikZ \foreach loop with macro-defined list I have a small problem with the TikZ \foreach loop whenever the list, over which we loop, is defined my a macro. The following code example will show my problem:  \documentclass{scrartcl} \usepackage[utf8]{inputenc} \usepackage{tikz}  \begin{document} Picture one:  \begin{tikzpicture} \foreach \x/\y in {1.0/2.0, 3.0/4.0} \node[draw] at (\x,\y) {\x--\y}; \end{tikzpicture}  Picture two:  \newcommand{\mymacro}{1.0/2.0, 3.0/4.0} \begin{tikzpicture} \foreach \x/\y in {\mymacro} \node[draw] at (\x,\y) {\x--\y}; \end{tikzpicture} \end{document}   The expected result is that both images should look the same. But in the second image, I only get one node - and both \x and \y are each time expanded to 1.0/2.0, 3.0/4.0. I hope someone can help. C non-blocking keyboard input I'm trying to write a program in C (on Linux) that loops until the user presses a key, but shouldn't require a keypress to continue each loop.  Is there a simple way to do this? I figure I could possibly do it with select() but that seems like a lot of work.  Alternatively, is there a way to catch a ctrl-c keypress to do cleanup before the program closes instead of non-blocking io? adb device doesn't listed on cmd {Lenovo K8 Plus} I am trying to root my Lenovo K8 Plus after unlocking bootloader. I try to install TWRP and somehow the TWRP recovery doesn't open and the phone is struck in the bootloop. I then fastboot the device and connect to PC and open minimal fastboot cmd. The phone wasn't listed in adb device, but listed in fastboot devices. I think usb debugging is not turned on because the system doesn't restart (maybe there is no ROM). What should I do? Why Listen to Music, why not Listening Music Maximum time I face this problem by saying listening music. Is there any traditional cause behind this?  Can we use listen music or listening music?  Seems there is only a slight difference, but why is listen to music the right way to say it?