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In this paper we show that the point-group (geometrical) symmetry isinsufficient to account for the degeneracy of the energy levels of the particlein a cubic box. The discrepancy is due to hidden (dynamical symmetry). Weobtain the operators that commute with the Hamiltonian one and connecteigenfunctions of different symmetries. We also show that the addition of asuitable potential inside the box breaks the dynamical symmetry but preservesthe geometrical one.The resulting degeneracy is that predicted by point-groupsymmetry.

On the symmetry of the quantum-mechanical particle in a cubic box