So for fermions they must be antisymmetric so would there just be N states since the second particle's state will have to be antisymmetric to the first?
For bosons would it be 2N?
My thoughts are:
a) it should just be N^2
b) just N since they're identical
c) due to Pauli exclusion would it be N^2 - N since they have to be different states?
I tried plugging Psi into the right of the Schrodinger equation but can't get anything close to the solution or anything that is usable. How should I solve this?