Quantum Mechanics degeneracies in 3d potential

[Slightly]

Homework Statement

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?

Homework Equations

n/a

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?

 

[RomegaPRogRess]

You can directly find the degenerate energy levels for an infinite cubic well. It's a worthwhile exercise.

The attempt at a solution is only valuable to understand that directions and their wavefunctions aren't unique for a cubically symmetrical potential.