Eigenvalue bounds for a class of Schroedinger operators in a strip

TL;DR

This paper develops bounds on the number of negative eigenvalues for Schrödinger operators in a strip, using weighted norms of the potential, including cases supported on embedded curves.

Contribution

It introduces new eigenvalue bounds for Schrödinger operators in a strip, considering potentials with specific weighted norm conditions and those supported on embedded curves.

Findings

Derived bounds involving weighted L^1 and L ln L norms of the potential.

Extended estimates to potentials supported on embedded curves.

Provided analytical tools for estimating bound states in strip geometries.

Abstract

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schroedinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L^1 norms and L ln L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in the strip are also presented.