Fermion Wavefunctions: Exchange Symmetry Explained

[captainjack2000]

Homework Statement

I was trying to work through some quantum physics questions and I was getting a bit confused. I know that for fermions the wavefunction must consist of spin and spatial parts of the fermionic wavefunction with opposite exchange symmetry (ie antisymmetric spin and symmetric spatial or antisymmetric spatial and symmetric spin) but I am a bit confused where the inital idea for the need for a overall antisymmetric wavefunction came from?

thanks

 

[kuruman]

It came from the Pauli Exclusion Principle. If you force two particles to have the same wavefunction in an antisymmetric combination, the two-particle wavefunction vanishes in accordance with the exclusion principle.

Example

Ψ = ψ_α(1)ψ_β(2) - ψ_β(1)ψ_α(2)

is an antisymmetric function. What do you get for α = β ?