The question I'm struggling to get out is to say if you have a wave function that is bounded on three dimensions with a specific energy, will you at maximum have 3 different separated Schrodinger's Eq, and of those maximum versions have 3 quantization conditions for each dimension. Which implies...
If ψ is normalize-able and a function of nx, ny, nz, is the maximum energy degeneracy 6?
I.E. There can be degeneracy at the same Energy with each state taking a different value of n, yet adding up to some (nx^2+ny^2+nz^2)=Same E, due to the linearity of the operators involved. I guess the...