Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip
Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> norms and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>L</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">ln</mml:mi></mml:mrow><mml:mo></mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math> norms of the potential. Estimates involving the norms of the …