Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip

Abstract

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and Lln⁡L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.