Novel expression for the wave function of a decaying quantum system

We report on a novel, practical method of determining the nonrelativistic w ave function of a decaying quantum system at all positions and times. The s ystem 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 psi(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 sca ttering S matrix of the system. The psi(r, t) so obtained is normalizable. In the light of this approach we reexamine the Gamow wave function, which i s not normalizable. We elucidate the source of this difficulty.