Analytical approach to the wave function of a decaying quantum system

Recently we outlined an analytical method of Solving the time-dependent Schrödinger equation for a model which simulates a decaying quantum system such as an α-decaying nucleus. A particle in the model is initially confined around the origin and leaks out, tunneling through a potential barrier. The solution can be expressed as a linear combination of the Moshinsky functions, each of which is associated with a pole of the Scattering S matrix of …