Spectral inequalities for Schroedinger operators with surface potentials

TL;DR

This paper establishes sharp spectral inequalities for Schrödinger operators with surface-supported potentials, linking these results to relativistic operator inequalities, advancing understanding of spectral bounds in quantum mechanics.

Contribution

It introduces new sharp Lieb-Thirring inequalities for surface-supported potentials and connects them to relativistic Schrödinger operator inequalities.

Findings

Proved sharp Lieb-Thirring inequalities for surface potentials.

Established relationships between surface potential inequalities and relativistic Schrödinger operators.

Enhanced spectral bounds for quantum systems with surface interactions.

Abstract

We prove sharp Lieb-Thirring inequalities for Schroedinger operators with potentials supported on a hyperplane and we show how these estimates are related to Lieb-Thirring inequalities for relativistic Schroedinger operators.