Blamo_slamo
Nov11-09, 10:52 PM
1. The problem statement, all variables and given/known data
If we were to ignore the interelectronic repulsion in helium, what would be it's ground state energy and wave function?
2. Relevant equations
I have created my ground state wave function \psi for 1s:
\psi = (1/\sqrt{}\pi)(z/a)3/2(e-zr/a)
The operator is the laplacian, in spherical polar coordinates.
3. The attempt at a solution
So the energy of the two particles is the hamiltonian operating on \psi,
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 = [(-\hbar 2/2m)(1/\sqrt{}\pi)(z/a)3/2](z2/a2 e-zr/a - 2z/ar e-zr/a) + V(r)\psi
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!
If we were to ignore the interelectronic repulsion in helium, what would be it's ground state energy and wave function?
2. Relevant equations
I have created my ground state wave function \psi for 1s:
\psi = (1/\sqrt{}\pi)(z/a)3/2(e-zr/a)
The operator is the laplacian, in spherical polar coordinates.
3. The attempt at a solution
So the energy of the two particles is the hamiltonian operating on \psi,
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 = [(-\hbar 2/2m)(1/\sqrt{}\pi)(z/a)3/2](z2/a2 e-zr/a - 2z/ar e-zr/a) + V(r)\psi
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!