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

Brice Camus
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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.

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Brice Camus. 2005-04-22. Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate potential. https://arxiv.org/abs/math-ph/0406058

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