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. T
he 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 depend
ent 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.