Resonant uniqueness of radial semiclassical Schrodinger operators

TL;DR

This paper proves that for certain radial, rapidly decaying potentials in odd-dimensional spaces, the resonances uniquely determine the potential among all similarly decaying potentials, highlighting a key inverse spectral property.

Contribution

It establishes the resonant uniqueness for radial, superexponentially decaying potentials in odd-dimensional spaces, a novel result in inverse spectral theory.

Findings

Resonances uniquely determine the potential in the specified class.

The result applies to superexponentially decaying, radial, monotonic potentials.

The proof extends inverse spectral theory in semiclassical Schrödinger operators.

Abstract

We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical Schrodinger operator among all superexponentially decaying potentials in R^n.