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

Article type: Research Article

Authors: Siedentop, Heinz^{; ;} | Weikard, Rudi

Affiliations: Matematisk institutt, Universitetet i Oslo, Postboks 1053, N-0316 Oslo, Norway | Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

Note: [] Dedicated to Adolf Max Klaus Müller on his 60th Birthday

Note: [] Correspondence to: H. Siedentop, Matematisk institutt, Universitetet i Oslo, Postboks 1053, N-0316 Oslo, Norway.

Abstract: We prove that the semi-classical expression for the sum of the negative eigenvalues of a one-dimensional Schrödinger operator with negative potential −φ is correct up to order O(h log 1/h) in the “Planck” constant h provided φ1/4 is in the Sobolev space H1(R).

DOI: 10.3233/ASY-1994-8104

Journal: Asymptotic Analysis, vol. 8, no. 1, pp. 65-72, 1994