RELATION BETWEEN DECAY AND DELAY TIMES

The concept of decay time is almost as old as quantum mechanics, while that of delay time is easily formulated in classical mechanics if the energy of the particle is greater than the height of the potential. The purpose of this note is to propose a quantum mechanical definition of delay time for a potential V(r) using the solution of a time dependent Schrodinger equation with a given initial condition. In particular we consider the 3-dimensional case V(r) = bdelta(r - 1) and for b >> 1 obtain explicitly the delay time as a linear function of b2.