GROUND STATES OF THE SCHRODINGER-MAXWELL SYSTEM WITH DIRAC MASS: EXISTENCE AND ASYMPTOTICS

We study a non-relativistic charged quantum particle moving in a bounded open set Omega subset of R(3) with smooth boundary under the action of a zero-range potential. In the electrostatic case the standing wave solutions take the form psi(t, x) = u(x) e-(iwt) where u formally satisfies -Delta u + alpha phi u - beta delta(x0) u = wu and the electric potential phi is given by - Delta phi = u(2). We introduce the definition of ground state. We show the existence of such solutions for each beta > 0 and the compactness as beta -> 0.