A quantum particle in a cubic box

We study the role of O point group symmetry on the wave functions of a quantum particle in a cubic box, for which the potential energy is zero inside the box and infinite outside it. In order to picture the low-energy wave functions, we use a Mathematica moving script that rotates the cube slowly enough that one can decide whether a given possible wave function obeys all of the symmetry operations of the point group. The rules for allowable wave functions with quantum numbers $(n_1,n_2,n_3)$ are determined and the a set of low-energy wave functions will be shown in color-coded movies of rotating boxes.