On finiteness of the sum of negative eigenvalues of Schroedinger operators

2008/02/14 by Michael Demuth, Demuth, Michael, Guy Katriel +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:35J10 #msc:35P15 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.0802.2032

arxiv created 2008/07/03 · arxiv updated 2009/12/01

Abstract

We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences and on complex analysis

Related

• Lower bounds on the eigenvalue sums of the Schrödinger operator and the spectral conservation law
• An upper bound for the number of eigenvalues of non-selfadjoint Schrödinger operator
• Negative spectrum of Schrödinger Operators with Rapidly Oscillating Potentials
• Number of eigenvalues for a class of non-selfadjoint Schrödinger operators
• Bound on the number of negative eigenvalues of two-dimensional\n Schr "odinger operators on domains