Birkhoff Normal Forms in Semi-Classical Inverse Problems

TL;DR

This paper leverages advanced semi-classical trace formulae and Birkhoff normal forms to address a broad class of spectral inverse problems at high energies, enhancing understanding of quantum spectral data.

Contribution

It introduces novel applications of semi-classical trace formulae and Birkhoff normal forms to solve inverse spectral problems in quantum mechanics.

Findings

Extended semi-classical trace formulae for inverse problems

Application of Birkhoff normal forms to spectral analysis

Improved methods for high energy spectral reconstruction

Abstract

We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.