- #1
Blamo_slamo
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Homework Statement
If we were to ignore the interelectronic repulsion in helium, what would be it's ground state energy and wave function?
Homework Equations
I have created my ground state wave function [tex]\psi[/tex] for 1s:
[tex]\psi[/tex] = (1/[tex]\sqrt{}\pi[/tex])(z/a)3/2(e-zr/a)
The operator is the laplacian, in spherical polar coordinates.
The Attempt at a Solution
So the energy of the two particles is the hamiltonian operating on [tex]\psi[/tex],
and I should get an eigen function out which would be the energy for one of the two particles.
Using the laplacian operator I got:
E = [(-[tex]\hbar[/tex] 2/2m)(1/[tex]\sqrt{}\pi[/tex])(z/a)3/2](z2/a2 e-zr/a - 2z/ar e-zr/a) + V(r)[tex]\psi[/tex]
For the energy of the one particle. My problem is,
that this isn't an eigen function of the laplacian, and I've managed to hit a brick wall.
I'm completely stumped on what I could do, any help would be greatly appreciated!