# Homework Help: Show that the total eigenfunction must be antisymmetric

1. Apr 20, 2017

### tarkin

1. The problem statement, all variables and given/known data

By considering the eigenfunctions for 2 noninteracting particles at distances r1 and r2,
show that their total eigenfunction must be antisymmetric.
.
2. Relevant equations

Spatial wavefunctions:

Ψ(x1,x2) = 1/√2 [ ψA(x1B(x2) ± ψA(x2B(x1)]

Where + gives a symmetric wavefunction and - gives an antisymmetric one.

3. The attempt at a solution

Hi, not really sure what to do with this one. I know that the Pauli exclusion principle says that the total eigenfunction must be antisymmetric for fermions. But the question doesn't mention fermions, just "2 noninteracting particles". I also know that the antisymmetric spin wavefunctions are associated with the symmetric spatial wavefunctions, and vice versa, to produce a total antisymmetric wavefunction, but I don't get why, which is what the question seems to be asking...

2. Apr 21, 2017

### Staff: Mentor

The question is very poorly worded. The wave function is anti-symmetric with respect to what? Bad questions have no good answers

3. Apr 21, 2017

### tarkin

Hi, sorry, I should probably have said a bit more in my OP. Presumably, in the question, the 2 particles are indistinguishable. So it means that eigenfunction must be antisymmetric under particle exchange. ie. that if the particles are swapped, this will give the negative of the original eigenfunction