Novel Expression for the Wave Function of a Decaying Quantum System

We report on a novel, practical method of determining the nonrelativistic wave function of a decaying quantum system at all positions and times. The system consists of a particle which is initially confined around the origin and leaks out tunneling through a potential barrier. We show that the wave function ψ(r,t) of the particle can be expressed as a linear combination of Moshinsky functions, each of which is associated with a pole of the scattering S matrix of the system. The ψ(r,t) so obtained is normalizable. In the light of this approach we reexamine the Gamow wave function, which is not normalizable. We elucidate the source of this difficulty.