I am working on a simple example of how to numerically solve the time-independent Schrodinger Equation for the infinite square well. I've used the Euler Method to find values of the wave function, $\psi (x)$, but now I've just realized something - I have no clue how to determine the energies from this! I know that analytically this comes down to applying the Hamiltonian to the wavefunction, but how do I find the energies numerically??  I can provide more info if needed.
This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the  and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done.  I've solved some initial value problems in the past using iterative methods such as Runge–Kutta. I've read that  is the way to solve Schrödinger's equation but Wikipedia also describes it as an iterative method for initial value problems.  How do I use it to solve an eigenvalue problem?  This confuses me for the following reasons:   Wouldn't iteratively solving the DE require knowledge of the energy eigenvalues to use as input to the calculation? I don't know the eigenvalues yet; they're precisely what I'm trying to calculate. If I did that, wouldn't I simply get a unique solution, instead of a family of eigenfunctions and eigenvalues?    I've seen some mention of "tridiagonal matrices" being generated somehow, but am not sure what the elements of that matrix would be or how that applies to the problem. Leandro M. mentioned that "the discretization defines a finite dimensional (matrix) eigenvalue problem". This seems like the correct road I should be going down, but I haven't been able to find anything that explicitly explains this process or how the matrix is constructed. If this is the correct procedure, how is such a matrix constructed?
Is there a way of installing Ubuntu (Windows Subsystem for Linux) on Win10 (v1709) without using the Store? The Microsoft Store app is disabled by Group Policy by my university. I have administrator rights on my computer and I was wondering if there was a way of installing Windows Subsystem for Linux (WSL) directly? Or maybe via Chocolatey or some other command line method? I would like to download and install the Ubuntu  on windows without using the Microsoft store.  Note that since version 1709 (Fall Creator's Upgrade), only enabling Developer Mode is no longer sufficient. Inhumans vs. Mutants in the Marvel Universe What's the difference between those two? Aren't Inhumans supposed to be an evolution of the human race "forced" by the Kree? Which is almost the same as Mutants, the natural evolution of the human race...  What exactly am I missing? XML - Data At Root Level is Invalid How do you create a dropdownlist from an enum in ASP.NET MVC? I'm trying to use the Html.DropDownList extension method but can't figure out how to use it with an enumeration.  Let's say I have an enumeration like this:  public enum ItemTypes {     Movie = 1,     Game = 2,     Book = 3 }   How do I go about creating a dropdown with these values using the Html.DropDownList extension method?  Or is my best bet to simply create a for loop and create the Html elements manually? How to find the matrix of a quadratic form? I was wondering. If I have a bilinear symmetric form, it is easy to find its matrix. But, when I have a quadratic form, which is the procedure to do that?  I heard that one possibility is: If $q$ is my quadratic form, then $$f(x,y) = \frac{1}{4}q(x+y) - \frac{1}{4}q(x-y)$$ is the bilinear symmetric form associated, so the method reduces to find the matrix of $f(x,y).$   The point is that seems a little noising... How to find, in practice, the matrix of quadratic form?  Thanks in advance. Can anyone tell me the name of these sentences? Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)?   Here is an example: 5! = 120.  Is there a way I can work out the number that must be factorialed (??) to give the answer 120? Custom attributes - Yea or nay? Getting Joker from the existing groups in Rummikub I have a group of tiles made up of 3 fours and a joker:     4 4 4 Joker   Now, if a player removes the joker, do they have to replace it with another 4? Asymptotic behavior of a trigonometric series Consider the following series $$S_N = \sum_{k=1}^N \frac{\sin[k\pi/(N+1)]}{k}.$$ What is the asymptotic behavior of this series for $N \to \infty$?  If we replace the sine function with the factor $1$, we get the standard harmonic series which diverges $\sim \ln N$. However, if we replace the sine function with $(-1)^k$, we get a convergent series with the result $\ln 2$. Therefore, I think that $S_N$, defined above, should diverge, but more slowly than the logarithm. Am I correct? Title page line spacing I have a simple problem but I didn't manage to find any answer for it. In my title page, I just used  \title{Name of the title}   then  \hrule height 0,1cm \leavevmode \\[0,5cm]     {\Huge{\textbf{\@title}}}\\[0,5cm] \hrule height 0,1cm \leavevmode \\[0,5cm]   to print the title of my document. But it takes more than 3 lines on the PDF file, and I have a different spacing between the 1st and 2nd line compared to the 2nd and 3rd, which is a bit frustrating.   Anyone got an idea of why ? I am looking for a transparent screensaver. Or a way for there to be no screen saver, but instead of locking, it disables the mouse and most of the keyboard, until I hit an unlock key. Why does virtualbox only have 32-bit option, no 64-bit option on Windows 7? I have downloaded and installed the newest  for my Windows 7 (64-bit OS), but when I want to install 64-bit Linux, the New->Create Virtual Machine only displays 32-bit option, no 64-bit option. Could anyone give any clues about this issue? Thanks very much in advance! Is it "to play a game on someone" or "play games with someone"? I find this expression strange because it's clearly widely used, but seems sort of "unofficial", the "official" version, meaning the one described in dictionaries and grammar books, being playing games with, not on.  Both expressions seem to be current and valid, according to Google Books. I'm just not entirely clear on the context and the usage.  My understanding is that playing games with implies some sort of tricky, mischievous behavior, which may or may not be intentionally malicious, like office politics or standing someone up on a date ("Jane didn't show up...again. Is she playing games with me?"), while playing games on implies a form of studied deception. ("The ad said that the comic book was in mint condition but there are barely noticeable tears... are they trying to play a game on me?") How do I do a case-insensitive string comparison? Sorry, I'm still a newbie to blender, but why are some edges visible only in edit mode, but not in wireframe view? is it a bug or am I missing something here?  edit mode: Edges visible. Object mode, wireframe view: Pooff, they're gone. what can i do to fix this? / thanks What limitations does converting question links to links with titles have? On this  there are more than 50 links to Stack Overflow questions. However, the last 6 links aren't converted to titles (http://facebook.stackoverflow.com/questions/6530420/control-the-image-that-facebook-shows-when-i-like-a-url should be converted to ).   However:  all http://facebook.stackoverflow.com/... into http://stackoverflow.com/... fixes this, both in the preview and the final result. Also, the preview won't show any title for http://facebook.stackoverflow.com/... links.  My question is, what limitations does this converting have? How are these question titles retreived? Via API? Through database?  I'm not sure about title, feel free to edit that I have a final exam tomorrow for fluid mechanics and I was just looking over the practice exam questions. They do not provide solutions. But pretty much I have to define pressure at a point and also say why pressure is scalar instead of a vector.  I am thinking pressure at a point is $P=\lim_{\delta A \to 0} \frac{\delta F}{\delta A}$. Please let me know if I am wrong.   But I do not know at all why pressure is a scalar instead of a vector. I know it has something to do with $d \mathbf{F}=-Pd \mathbf{A}$ Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? How to correctly enable Desktop Cube in Unity 3D? I have read several questions regarding how to fix an already enabled desktop cube or the problems it had in 11.04. But in 11.10, how can I correctly enable desktop cube in Unity 3D?