Slater Determinant & Permanent

[M. next]

How to use Slater determinant and permanent to find out whether the state is symmetrical or anti-symmetrical?
How to use them? I got the concept but I didn't get for example when to know if there was a plus or a minus and thus whether what we're talking about is a permanent or determinant (respectively).

 

[cgk]

If you have minus signs, its a determinant and totally antisymmetric, if you don't, it's a permanent and totally symmetric.

It's not something you determine. It is something you put into your ansatz: You choose determinants as a basis set for fermionic systems precisely because you know that you need an antisymmetric wave function, and determinants are the simplest kinds of wave functions which are totally antisymmetric. And for the same reason you choose permanents as basis for bosonic systems because they are the simplest wave functions which are totally symmetric.

 

[M. next]

Thank you a lot for clearing things up. I thought it is something to be determined.