2 electrons are in a box of length L. Ignoring Coulomb force, 1 and 2 are labels for the electrons and m is the mass of an electron. What is the ground state and 1st excited state for the energy and wavefunction for the two electrons? Is there more than one wavefunction for the ground state and the 1st excited state? Your answer will include the spatial and spin components of hte wavefunction. Use |+-z> to describe spin.
The Attempt at a Solution
Since they are electrons, they are spin 1/2 particles and are fermions. Thus, their wavefunction must be antisymmetric with repsect to the exchange of particle labels. This means the two particles have a total spin of 0 or 1, so there are two wavefunctions for the ground state?
S=0: |0,0,s=0,m=0> and S=1: |0,1,s=0,m=0>. Am I on the right track here?