Quantum mechanics and Talbot revivals on a tetrahedron

Abstract

We analyze the propagation of waves on the surface of the simplest Platonic solid, the regular tetrahedron. We find that the time evolution of a quantum particle confined to such a surface is equivalent to the diffraction pattern from a certain grating profile and can therefore be investigated in a simple diffraction experiment. The quantum particle exhibits perfect quantum state revivals, which translate into the fractional Talbot effect in the diffraction pattern. We present the results of such an experiment and compare them with numerical simulations.