# Homework Help: Molecular orbital wavefunctions

1. Feb 7, 2008

### gazepdapi1

[SOLVED] molecular orbital wavefunctions

http://img255.imageshack.us/img255/7012/37626561fb6.jpg [Broken]

starting with

Sz(total) = Sz1 + Sz2
Sz(alpha) = +(1/2)hbar(alpha)
Sz(beta) = -(1/2)hbar(beta)

I first found the determinant and then simplified

psi = 1/sqrt(2)psi(b)^2[alpha(1)beta(2) - alpha(2)beta(1)]

So,

Sz1psi = 1/sqrt(2)psi(b)^2[beta(2)(1/2)h(bar)alpha(1) + alpha(2)(1/2)h(bar)beta(1)]

Sz1psi = 1/sqrt(2)psi(b)^2[-alpha(1)(1/2)h(bar)beta(2) - beta(1)(1/2)h(bar)alpha(2)]

So...
Sztotal = Sz1 + Sz2 = 0

Can someone please verify if this is correct?
I would appreciate it.
thank you

Last edited by a moderator: May 3, 2017
2. Feb 9, 2008

### gazepdapi1

I realize it's hard to read without the LaTeX, but no one can check if it's correct or not?

3. Feb 9, 2008

### malawi_glenn

yes it seems to be ok,

learn LaTeX, it is worth it :)

4. Feb 9, 2008

### kdv

I don't understand that result. Shouldn't the second term be negative since it's a beta?

You means Sz2 I think here. But the second term should be positive since it's an alpha, no?

Last edited by a moderator: May 3, 2017
5. Feb 9, 2008

### gazepdapi1

No because when you multiply by the -(1/2)hbar, the beta portion (the second term) becomes a positive, the opposite goes for the alpha, I think, and yes it should be an Sz2.

6. Feb 9, 2008

### kdv

you are absolutely right, my mistake. For some reason, when i replied to your post, I forgot about the Slater determinant and I was thinking about a symmetric wavefunction. Sorry about that.

7. Feb 9, 2008

### gazepdapi1

Thank you all for your help