# Hamiltonian matrix for two electrons in a 1D infinite well

1. Jan 25, 2016

### nothingisreal

Hi everyone,
I need help for preparing a Hamiltonian matrix.

What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well):

$-\frac{ħ^{2}}{2m}$$(\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) + \frac{q}{4πε_0ε_r(x_1-x_2)}ψ(x_1,x_2)=Eψ(x_1,x_2)$

[probably the problem is an intermediate level problem. I mistakenly selected advance level. And, now I can't edit it]

Thank you very much in advance......
:)

Last edited: Jan 25, 2016
2. Jan 25, 2016

### Dr. Courtney

The matrix elements depend on the choice of basis.

A reasonable choice of basis might be the solution of a single electron in the infinite well, that is considering the infinite well with one electron as the unperturbed problem and the second electron as the addition.

However, perturbation theory doesn't work well when the additional term in the Hamiltonian (the perturbation) can be comparable to or larger than the original terms.

This forum has discussed similar problems before:

https://www.physicsforums.com/threa...f-two-electrons-in-a-1-d-infinite-well.15277/