Linked Questions

50
votes
5answers
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 ...
18
votes
5answers
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 ...
21
votes
2answers
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 ...
13
votes
1answer
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 ...
3
votes
2answers
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 ...
10
votes
2answers
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 ...
6
votes
1answer
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 ...
4
votes
2answers
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}\...
2
votes
0answers
932 views

Schrödinger equation for Hydrogen atom [closed]

I'm trying to solve Schrödinger 1D equation for hydrogen atom but I found several difficulties. To get in context I want to solve this equation For Z and l real and arbitraries. To start with I ...
9
votes
0answers
439 views

Solving the 2D Schrödinger equation with eigensystem, then verifying orthonormality of eigenfunctions with NIntegrate

I am solving the time-independent 2D Schrödinger equation for an interacting electron and hole in the case of anisotropic electron and hole masses, where the interaction is described a modified form ...