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 Schrodinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted 𝐿1 norms and 𝐿 ln 𝐿 norms of the potential. Estimates Involving the norms of the potential supported by a curve embedded in a strip are also presented.