Any quantum state must be a square integrable function in order for it to be allowed. Is there any reason that this should be so? As far as I am aware, other $L^p$ spaces can have norms defined on them in a similar way to the norm of $L^2$.  Is it just experimental fact that the probability of a position measurement, say, is given by$\int |\phi (x)| dx$, or is there some more foundational reason to restrict quantum states to $L^2$.  I apologize if I am unclear, I feel like I may be missing something fundamental here.
I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space of state functions, from where this arises? and why 2-order space that assumes the following inner product:  $\langle\phi|\psi\rangle =\int\phi^{*}\psi\,dx$  While there is many ways to define the inner product.  In Physics books, this always assumed as given, never explains it, also I tried to read some abstract math books on this things, and found some concepts like "Metric weight" that will be minimized in such spaces, even so I don't really understand what is behind that, so why $L_2$? what special about them? Who and how physicists understood that those are the one we need to use?
What kind of distribution is this "almost" uniformly distributed data for calls/week? My supervisor asked me to find out which distribution represents a particular situation.  I have a VoIP generator that generates calls "uniformly" distributed between callers. This means that the volume per caller distribution is "almost" uniformly distributed between a minimum and maximum. So by running a test with 10000 users and a min value equal to 30 calls per week and a max value equal to 90 calls/week i obtain that not all the users respect this limits: we have some users that generate &lt;30 calls and some other users that generate >90 calls. It is clear that the obtained distribution is not uniform.  The situation is this:    He said that i have to perform a sort of numerical process in order to find some formulas that could define this distribution. Initially, as wrote before,we wanted to obtain a uniform (min,max) distribution (the green area in the figure) but this is not the case as proved with chi-square test.  Moreover the curve in figure is not symmetric, the probability of call generation below 30 call/week and greater that 90 call/week are not identical (it is high for 90calls/week). The variability of the number of generated call increases with the increasing call generation rates.   "Actually implementation of this distribution is nothing but assigning different call rates in a range for users in domain which indicates implementation of several delta functions. As the call rates increases the variability of the generated calls also increases with the average call rate and this leads to the asymmetric behavior of the curve." [cit. from the Voipgenerator documentation]  Someone can help me?I think that now i cannot use Q-Q plot because i don't know which theoretical distribution i have to use in order to compare it with my empirical data.  Sorry if I have stressed with a similar problem a few weeks ago, but initially we thought we could change the implementation, but now we cannot. Hence i have to discover the type of the distribution i obtained and i don't know how can i do this. Using past tense when referencing a still-true fact In the sentence: "I didn't know she had a son,"   Can I say "I didn't know she has a son" instead, because he is a teenager now?  Or are both correct? SciFi movie (or miniseries) of the afterlife I am trying to find the name of a direct to TV movie, possibly a 2-3 part miniseries which I believe aired on the SciFi channel in the 90s. I don't remember who starred in it, but the movie opened with an astronaut attempting reentry whose shuttle ends up exploding. He awakes in a large bubble of air in a river and after reaching the surface and swimming to shore, meets several other people, from seemingly many different times throughout history (including one alien, who died on Earth).  Over the course of the movie, we learn the world is the afterlife, where everyone goes when they die. The major plot involves launching a steamboat (built by Mark Twain, no less) to travel up a river to the mountains, where the beings responsible for bringing everyone to this world are.  Does anyone know what the title of this movie/miniseries is? Dr Math told his family to write 4 different integers from 1 to 9 on to the 4 ] Why don't the White Walkers take the sea route to Westeros After watching 6 seasons of Game of Thrones, we know that the only roadblock for White Walkers is "The Wall" to stop them from attacking Westeros. However, we see that King Stannis attacked wildlings through a ship route without crossing the Wall.  What is stopping the White Walkers from doing the same? They can ask wights to make Ships or rowboats. They have a lot of forests to get wood for making ships. They can simply land at the coast of the North and attack Winterfell or whatever they want. I just saw now that a new build had rolled out in which the comment upvote and flag options are always visible. Previously, one had to mouse over the area in order to see them.  Why was this just changed? Is it to support touch screens? I'll admit, it was difficult to find the flag button using my touchscreen laptop running Microsoft Edge.  Cross-site duplicate on MSO: Where is the ideal place to ask a MATLAB question? I'm confused with using single or double brackets. Look at this code:  dir="/home/mazimi/VirtualBox VMs"  if [[ -d ${dir} ]]; then     echo "yep" fi   It works perfectly although the string contains a space. But when I change it to single bracket:  dir="/home/mazimi/VirtualBox VMs"  if [ -d ${dir} ]; then     echo "yep" fi   It says:  ./script.sh: line 5: [: /home/mazimi/VirtualBox: binary operator expected   When I change it to:  dir="/home/mazimi/VirtualBox VMs"  if [ -d "${dir}" ]; then     echo "yep" fi   It works fine. Can someone explain what is happening? When should I assign double quotes around variables like "${var}" to prevent problems caused by spaces? Why would var be a bad thing? I think it's well established that for the basic premise in the Back to the Future Trilogy to work, we have a system of alternate timelines.  If this is the case though, then why would Marty in Back to the Future (the original) begin to fade?  Logically, there would simply be no Marty in the alternate timeline created when Marty travels back to 1955 for the first time; why should this affect the original Marty from the original timeline? Change desktop background to a solid color (e.g. pitch black) in GNOME 3 Esaki effect implementation on simple oscillator circuit I am trying to learn basic oscillator circuits with the help of this   But when I connected the components, my LED is not blinking. Rather, it is giving bright light.  The components I have used are 1K resistor 18V battery 200uF capacittor 2N2222 transistor and LED with 100 ohm resistance.  Here is the circuit:      From above page: The difference between a poor or meh question and a stellar question can often simply be someone understanding it and providing it a great answer. I can't begin to count the number of times I've justified re-opening a question as a moderator by saying:     Look at the answer it got, though. This isn't something we want deleted, this is something we want fixed, because it's obviously valuable. Someone with domain knowledge can easily edit that question based on the answer it received.   This doesn't only apply to borderline-poor or poor questions – sometimes a good edit means the difference between 100 and 10,000 people finding something through typing things into Google. Good titles are hard.   We think we've come up with a way to provide incentive for good, opportunistic edits to happen more often, ideally without questions needing to go through closure or collecting a centimeter of dust before they do. What if we simply rewarded folks that answered and edited questions with a special, relatively difficult to earn badge?  Let's say that you answer something, and:   You edit the question 12 hours before or after answering it. This allows you to edit now, answer later &mdash; or answer now and edit later, when you have the time. Your edit isn't rolled back, or outright rejected if it was a suggested edit The question is not closed for any reason, even simply being a duplicate Your answer has a score of 1 or higher   &hellip; then you've done something that we probably want to recognize. You understood something, you provided the knowledge that you have, and then you provided an edit to make sure that more people in need of this knowledge can find it, while raising the overall quality of the site.  Here's the proposed tiers for the badge (within the above stated criteria):   Explainer (Bronze): Answered &amp; edited 10  questions Refiner (Silver): Answered &amp; edited 50 questions Illuminator (Gold): Answered &amp; edited 500 questions   We think this is going to be pretty hard to game. You can't go leaving streaks of terse snark all over the place on questions you know are going to be closed anyway, and junk edits aren't going to fly.  We're talking about rewarding folks that take a tiny bit more time out of their day just to write a more descriptive title so that folks can find the awesome answer that they wrote. Just doing that alone can make a big difference. Sure, it's a tad hard to get at the gold level, but it's supposed to be. If you routinely edit questions that you answer and have done so for some time, you'd probably get it the day we roll it out.  While this is technically something that we came up with on the quality initiative ( | ) &mdash; this badge could be earned on all of our sites.  What do you think? What did we miss? What could be better about the idea? Display lines in last 10 minutes with specific pattern in logs I need to display lines with Error occurred in last 10 minutes of a log file.   Aug 26 10:50:42 Normal line. Aug 26 10:51:23 Normal line. Aug 26 10:55:33 Error line. Aug 26 10:56:45 Normal line. Aug 26 10:58:12 Error line. Aug 26 11:02:31 Normal line. Aug 26 11:03:32 Normal line. Aug 26 11:04:11 Normal line.   Suppose above sample of log file. I want to display only following two lines  Aug 26 10:55:33 Error line. Aug 26 10:58:12 Error line.   I am using AIX. Why do we use encrypt-decrypt-encrypt (EDE) in 3DES, rather than encrypting three times? I'm wondering why we use encrypt-decrypt-encrypt (EDE) sequence in 3DES (also known as DES-EDE, TDES or TDEA) with three keys instead of three times encryption (EEE) with three different keys? Let $f_n(x) : \mathbb{R} \rightarrow \mathbb{R}$ be defined as $\dfrac{x}{n}$. Is $f_n$ uniformly convergent?   With "$(a_n)$ is limited and $(b_n)$ converges to 0 $\Rightarrow (a_nb_n)$ converges also to 0" i would guess that $x\cdot \dfrac{1}{n}$ converges uniformly but $x$ is not limited in this case. So does ist converge uniformly or not? Why is my iron ore disappearing when mined with a wooden pickaxe? I am on Peaceful mode, and I am using a Wooden Pickaxe. Whenever I mine Iron Ore, it just disappears. Am I doing something wrong? P-adic expansion construction Fantasy Short Story that appeared in an anthology about 1968-1971 I read this short story around 1971.  The basic plot is for a steward to lead the king's son to another city state.  Along the way they have a number of interactions with people/subjects that demonstrate the immaturity of the son.  Last one involves the son beating up the suitor of a innkeeper's daughter.  When confronted by the steward, the son displays his contempt and chauvinistic regard of his future subjects and the steward kills him.  Turns out the trip was a test of his suitability to assume the crown and the steward explains to the king that he was not worthy.  Been looking in all the anthologies can seem unable to find it.  Thanks for your help How do I tell Maven to use the latest version of a dependency? In Maven, dependencies are usually set up like this:  &lt;dependency&gt;   &lt;groupId&gt;wonderful-inc&lt;/groupId&gt;   &lt;artifactId&gt;dream-library&lt;/artifactId&gt;   &lt;version&gt;1.2.3&lt;/version&gt; &lt;/dependency&gt;   Now, if you are working with libraries that have frequent releases, constantly updating the &lt;version&gt; tag can be somewhat annoying. Is there any way to tell Maven to always use the latest available version (from the repository)?