Semiclassical analysis of general second order elliptic operators on bounded domains

Abstract

In this work we ascertain the semiclassical behavior of the fundamental energy and the ground state of an arbitrary second order elliptic operator, not necessarily selfadjoint, on a bounded domain. Our analysis provides us with substantial improvements of many previous results found in the context of quantum mechanics for C ∞ C^\infty perturbations of the Laplacian.