The evolution operator for time-dependent potentials of zero radius (Q1080056)

The properties of the evolution operator corresponding to a system of potential wells of zero radius with time-dependent depth are studied. It is shown that the Schrödinger equation determining the evolution operator admits reduction to a system of Volterra integral equations for functions of a single variable (the time). Compactness of the difference of evolution operators obtained for two distinct dependence of the depths of potential wells on time is established.