Spectral uniqueness of radial semiclassical Schrodinger operators

Abstract

We prove that the spectrum of an n-dimensional semiclassical radial Schrödinger operator determines the potential within a large class of potentials for which we assume no symmetry or analyticity. Our proof is based on the first two semiclassical trace invariants and on the isoperimetric inequality.

9 pages. This is a revision which includes a new section about how to handle the critical energy levels