Symmetric/antisym solutions question

[Greger]

hey

i've been working on this question

http://img138.imageshack.us/img138/6457/gdgdad.jpg

the first two parts of the question seem easy enough, you just simple substitute the wave functions into the symmetric and anti-symmetric wave function definition.

ψ=ψ₁(1)ψ₂(2)±ψ₂(1)ψ₁(2)

Then the second part of the question you just take ψ*ψ for both cases.

there's two parts I am a little worried about,

Is the potential V=kr² irrelevant? it seems to be irrelevant to me but i just wanted to make sure.

i'm also not sure how to do 1c,

i would say that the symmetric wave function would have a larger expectation value since the wave function is

ψ_s=ψ₁(1)ψ₂(2)+ψ₂(1)ψ₁(2)

and not -, so it would be bigger, but I'm not sure if that is correct,

is V irrelevant and 1c as simple as i put it?

 

[M Quack]

The potential is relevant is so far as it defines the single-particle wave functions.

Finding these could have been the zero-th part of the question :-)

(a) Your solution for Psi_A,S looks right, except that it is not normalized.

(b) yup, watch out for the normalization.

(c) my guess is the opposite. Hint: Antisymmetric wave functions fulfill the Pauli exclusion principle.

(d) could have been to find the potential energy of the symmetric and antisymmetric wave functions. For that you need the potential again.