On some sharp spectral inequalities for Schr\"odinger operators on semi-axis

TL;DR

This paper derives sharp spectral inequalities for Schrödinger operators on semi-axis with matrix potentials, extending their application to star graphs and half-spaces with Robin boundary conditions.

Contribution

It introduces new sharp Lieb-Thirring inequalities for matrix-valued Schrödinger operators on semi-axis, applicable to various boundary value problems.

Findings

Established sharp Lieb-Thirring inequalities for matrix Schrödinger operators.

Extended spectral inequalities to star graphs and half-spaces with Robin boundary conditions.

Provided tools for analyzing spectral properties in related quantum systems.

Abstract

In this paper we obtain sharp Lieb-Thirring inequalities for a Schr\"odinger operator on semi-axis with a matrix potential and show how they can be used to other related problems. Among them are spectral inequalities on star graphs and spectral inequalities for Schr\"odinger operators on half-spaces with Robin boundary conditions.