Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials

TL;DR

This paper improves bounds on the number of bound states for matrix-valued Schrödinger operators using a functional integral approach, refining previous constants and advancing spectral analysis techniques.

Contribution

It introduces a sharper CLR-type bound for matrix-valued potentials employing Lieb's functional integral method, surpassing earlier constants by Hundertmark.

Findings

Established a new, improved bound on the number of bound states.

Demonstrated the effectiveness of the functional integral method for matrix potentials.

Provided tighter constants in spectral inequalities.

Abstract

We give a CLR type bound on the number of bound states of Schroedinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.