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.

  1. Is the ground state double-degenerate? Because I could exchange the spins and get a minus sign because of antisimmetry. Is this correct?
  2. 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,

  1. Ground state is non degenerate
  2. First excited state: non degenerate as well, because if I exchange two bosons nothing happens.

Thankyou for your help!

  • $\begingroup$ An overall minus sign is irrelevant, i.e. the wave function is the same wave function if it is multiplied by a minus sign. $\endgroup$ – march Mar 23 '16 at 17:28
  • $\begingroup$ Are the particles distinguishable or indistinguishable? $\endgroup$ – john Mar 23 '16 at 17:44
  • $\begingroup$ they are indistinguishable $\endgroup$ – Marco Mar 23 '16 at 18:01
  • $\begingroup$ @march , would this mean that in the fermions case, the ground state is non degenerate and the 1st excited is double degenerate? $\endgroup$ – Marco Mar 23 '16 at 18:03
  • $\begingroup$ Probably. To some extent, you haven't provided enough information. By "in a box", do you mean a 1D, 2D, or 3D box? Do the two different spin states have different energies? Are the bosons spin-0 or do they have some extra internal structure? Etc. $\endgroup$ – march Mar 23 '16 at 18:06

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