• Support PF! Buy your school textbooks, materials and every day products Here!

Wavefunction of 2 electron system

  • Thread starter jumphigh
  • Start date
  • #1
6
0

Homework Statement



Ignoring the repulsion force between two electrons, one of the electrons is in 1s state and the other is in 2p state. what is the total wavefunction of the system that is made up of the multiplication of the spatial wavefunctions and spin values?

Homework Equations



so, if electron(1) is in 1s state and e(2) is in 2p state, their spatial wavefunction will be :
u1(r1)u2(r2) - u1(r2)u2(r1)
with spins of
chi-(1) chi+2 and so on



The Attempt at a Solution



there are 8 possible products of spatial wavefcn and their spins for both electrons individually, I think there are only 4 combinations that are allowed by exclusion principle, those are:

{u1(r1)u2(r2) - u1(r2)u2(r1) }χ+(1) χ+(2)

{u1(r1)u2(r2) - u1(r2)u2(r1) }χ-(1) χ-(2)

u1(r1)u2(r2) {χ-(1) χ+(2) } - u1(r2)u2(r1) {χ-(2) χ+(1) }

u1(r1)u2(r2) {χ-(2) χ+(1) } - u1(r2)u2(r1) {χ-(1) χ+(2) }

Im not sure if the last combination is necessary, it kinda looks like the third one, any ideas? does the whole combination makes sense?

Thanks
 

Answers and Replies

Related Threads on Wavefunction of 2 electron system

Replies
4
Views
10K
Replies
13
Views
6K
Replies
8
Views
2K
Replies
3
Views
997
Replies
13
Views
2K
Replies
1
Views
1K
Replies
0
Views
1K
Replies
1
Views
3K
Replies
4
Views
702
Top