I need some hints about degeneracy. So, I consider an energy level degenerate if there are two distinct wave functions at that energy.
Then, let's say I have two spin1/2 fermions in a 1D box.
- Is the ground state double-degenerate? Because I could exchange the spins and get a minus sign because of antisimmetry. Is this correct?
- the first excited state is 4-degenerate? cause I can excite the spin up and then exchange getting a minus sign, and same for spin down.
If I have spinless bosons instead,
- Ground state is non degenerate
- First excited state: non degenerate as well, because if I exchange two bosons nothing happens.
Thankyou for your help!