Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate potential

Abstract

We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on ${\mathbb{R}}^n$. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result, which computes the contribution of this equilibrium, is valid for all time in a compact and establishes the existence of a total asymptotic expansion whose top order coefficient depends only on the germ of the potential at the critical point.

15 pages, minor changes

References in corpus (1)

• Contributions of non-extremum critical points to the semi-classical trace formula

Cited by in corpus (1)

• Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential