The resonance counting function for Schr\"odinger operators with generic potentials

TL;DR

This paper proves that for generic potentials, the resonance counting function of Schrödinger operators exhibits maximal growth, advancing understanding of spectral properties in quantum mechanics.

Contribution

It establishes that the resonance counting function reaches maximal order of growth for generic real or complex potentials in $L^ abla$-compact support.

Findings

Resonance counting function has maximal growth for generic potentials.

Results apply to both real-valued and complex-valued potentials.

Advances spectral theory of Schrödinger operators.

Abstract

We show that the resonance counting function for a Schr\"odinger operator has maximal order of growth for generic sets of real-valued, or complex-valued, $L^\infty$-compactly supported potentials.