25k views

### Find eigen energies of time-independent Schrödinger equation

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, $-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ where U(x) is some potential and Ei is the ...
3k views

### periodic boundary conditions and NDEigensystem

Mathematica 10 has a splendid new function, NDEigensystem, that makes it possible to solve Sturm-Liouville problems numerically in a single step. I have not however been able to find a way to get it ...
863 views

### Partial Differential Equation in Parallel

is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ...
1k views

### NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
797 views

### How to numerically solve the Schrödinger equation for Lennard-Jones potential?

Hi I have a potential like below: V[x_]:= 102*(4343/x^12 - 650/x^6) + 33/x^2 Which is a kind of modified Lennard-Jones potential. Schrödinger equation is 1D ...
983 views

### NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
843 views

### How to numerically solve a 1D time-independent Schrödinger equation for two interacting particles

Solving the 1D single-electron time-independent Schrödinger equation has been demonstrated using NDEigensystem here. There, the single-electron Schrödinger equation ...
249 views

### NDEigensystem and radial function equation for Hydrogen atom

I'm trying to numerically solve the radial equation for the 3D hydrogen atom problem, i.e., to find $R(r)$ which satisfies:  -\frac{\hbar^2}{2m}\left[\frac{1}{r}\frac{d}{dr}\left(r^2\frac{dR(r)}{dr}\...