Eigenvalue estimates for magnetic Schroedinger operators in domains

TL;DR

This paper derives inequalities for sums and quotients of eigenvalues of magnetic Schrödinger operators with non-negative electric potentials, capturing the correct semi-classical growth behavior.

Contribution

It provides new bounds for eigenvalues of magnetic Schrödinger operators that accurately reflect their asymptotic behavior in the semi-classical limit.

Findings

Derived inequalities for eigenvalue sums and quotients.

Bounds match the expected semi-classical growth.

Applicable to operators with non-negative electric potentials.

Abstract

Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.