Triplets and wave function


by Joqe
Tags: atoms, electrons, quantum mechanics
Joqe
Joqe is offline
#1
Nov24-09, 01:19 PM
P: 6
Hi

According top Hunds rule I have a [tex]^{3}P[/tex] term which should be the term for the ground state for a [tex]2p^{2}[/tex] shell (in this case the outer sub-shell), this means that I have a triplet state and thus a symmetric wave function for the spinn. Since the electrons are femions the total wave function should be anti-symmetric, this means that my spartial wave functions must be anti-symmetric.

My problem arises when I'm trying to construct a anti-symmetric spartial wave function and give it in Hydronic spatial wave function. I use

[tex]\psi_{spatial}=\frac{1}{\sqrt{2}}\left[\psi_{a}(1)\psi_{b}(2)-\psi_{b}(1)\psi_{a}(2)\right][/tex]

to create the anti-symmetric wave function. But quantum number [tex]{l} = {1}[/tex] for all the electron and quantum number [tex]{m_{l}} = {-1},{0},{1}[/tex] for all the electorns. This will lead to that the anti-symmetric wave function allways is equal to 0.

Can someone please help me?

Regareds
/Joqe
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