BOUNDEDNESS AND CONTINUITY OF THE FUNDAMENTAL SOLUTION OF THE TIME DEPENDENT SCHRODINGER EQUATION WITH SINGULAR POTENTIALS

Dedicated to Professor Kyuya Masuda on his sixtieth birthday

Abstract

We show that the fundamental solution of the initial value problem for the time dependent SchrÖdinger equation is bounded and continuous for a class of non-smooth potentials. The class is large enough to accomodate Coulomb potentials if the spatial dimension is three.