The semi-classical Weyl law on complete manifolds

TL;DR

This paper proves that the semi-classical Schrödinger operator with a growing potential on a complete Riemannian manifold follows the Weyl law, extending spectral asymptotics to this geometric setting.

Contribution

It establishes the Weyl law for semi-classical Schrödinger operators on complete manifolds with growing potentials, a novel extension of classical spectral theory.

Findings

Weyl law holds for semi-classical Schrödinger operators on complete manifolds.

Spectral asymptotics are valid under the given geometric and potential growth conditions.

Extends classical Weyl law results to a broader geometric context.

Abstract

We prove that the semi-classical Schrodinger operator with growing potential on a complete Riemannian manifold satisfies the Weyl law.