Show that the total eigenfunction must be antisymmetric

[tarkin]

Homework Statement

[/B]
By considering the eigenfunctions for 2 noninteracting particles at distances r1 and r2,
show that their total eigenfunction must be antisymmetric.
.

Homework Equations

Spatial wavefunctions:

Ψ(x₁,x₂) = 1/√2 [ ψ_A(x₁)ψ_B(x₂) ± ψ_A(x₂)ψ_B(x₁)]

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

The Attempt at a Solution

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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...

 

[DrClaude]

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

 

[tarkin]

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

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