Image method solutions for free-particle wave packets in wedge geometries

Using analogues of familiar image methods in electrostatics and optics, we show how to construct closed-form wave packet solutions of the two-dimensional free-particle Schrödinger equation in geometries restricted by two infinite wall barriers separated by an angle Θ_N = π/N. As an example, we evaluate probability densities and expectation values for a zero-momentum wave packet solution initially localized in a Θ₃ = π/3 = 60° wedge. We review the time development of zero-momentum wave packets placed near a single infinite wall barrier in the appendix.