1. The problem statement, all variables and given/known data What are the possible degeneracies and what is the symmetry of the position probability distribution in the case of a particle subject to a three-dimensional potential with cubic symmetry? 2. Relevant equations n/a 3. The attempt at a solution With a three-dimensional potential, there are 6 ways to look at the wave function. (x,y,z) (x,z,y) (y,x,z) (y,z,x) (z,x,y) (z,y,x) Those are the degeneracies. The symmetry of the position probability distribution relies on the weighted average of the wave functions. Is this correct or is there a more direct way to answer this?