Eigenvalue variations and semiclassical concentration

TL;DR

This paper investigates how the behavior of eigenvalues of a Schrödinger operator is influenced by the concentration of eigenfunctions in phase space, revealing a connection between spectral properties and phase space localization.

Contribution

It establishes a relationship between eigenvalue variations and semiclassical concentration of eigenfunctions, providing new insights into spectral analysis.

Findings

Eigenvalue behavior depends on eigenfunction concentration

Phase space localization influences spectral properties

Results connect semiclassical analysis with eigenvalue variations

Abstract

We show that the behaviour of analytic eigenbranches of a Schr\"odinger operator depends on the way eigenfunctions concentrate in the phase space.