Asymptotically correct lower bound for the sum of negative eigenvalues of Schrödinger operators through a decomposition of unity given by Macke

Abstract

Siedentop, H. and R. Weikard, Asymptotically correct lower bound for the sum of negative eigenvalues of Schriidinger operators through a decomposition of unity given by Macke, Asymptotic Analysis 8 (1994) 65-72. We prove that the semi-classical expression for the sum of the negative eigenvalues of a one-dimensional Schriidinger operator with negative potential -cp is correct up to order O(h log 1/h) in the Planck constant h provided cpl/4 is in the Sobolev space Hl(lRl.).