Quantum particle on the surface of a cube

We analyze the dynamics of a quantum particle on a force-free surface of a cube. Employing the methods of group theory, we divide the solutions of the stationary Schr"odinger equation (the modes) into classes based on irreducible representations of the symmetry group of the cube and for each class we reduce the problem to finding the modes on a square with special boundary conditions. We analyze the properties of the resulting modes, present them visually, and discuss the possibility of quantum state revivals on the cube.