History/Derivation of multi-particle wave functions?

[Jerbearrrrrr]

Hi,
it says on Wikipedia here that "a particle in state n, and a particle in state m" is described by
|n>|m>±|m>|n>
rather than the naive |n>|m>.

I can see why this is sensible on many accounts (eg, you'd want to preserve the predicted probability of finding blah under switching the indices, due to indistinguishability).

Where can I find a derivation of this? Or what should I read up on in order to understand it this better? Perhaps it comes from statistical mechanics or something?

Or is it just a neat "guess" that happens to agree with experiment? (Arguably all of physics is or comes from this, I suppose)

I'm not really sure what to google, but I have tried googling. Usually comes up with lecture notes that derive it by the argument of "We want our final answer to have these certain properties, so let's just take what we have so far from the Schrödinger equation and do this, that and the other to make it have those properties".

I have a maths degree from Cambridge, so I don't mind reading technical material involving equations...but I barely know any physics :(

Thanks,
and sorry for the disorganized post.

 

[azntoon]

The statement you have provided is called the exchange symmetry or exchange symmetry postulate. This postulate states that two indistinguishable particles with spin 1/2 (or any fermion), when exchanged, their wave function must change sign. This is also known as antisymmetry of the wave function.It can be derived from the Schrödinger equation of two particles in a single state. In this case, the exchange symmetry postulate states that the wave function of two particles in a single state must be antisymmetric. It then follows that for two particles in different states, the wave function must be of the form |n>|m>±|m>|n>, where the sign depends on the spin of the particles.For a detailed derivation of the exchange symmetry postulate, you may want to check out some textbooks such as Introduction to Quantum Mechanics by David J. Griffiths or Quantum Mechanics by John S. Townsend.