Eigenvalue bounds for two-dimensional magnetic Schroedinger operators

Abstract

We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We also show how the corresponding upper bounds depend on the properties of the magnetic field and discuss their connection with Hardy-type inequalities.

References in corpus (2)

• Equivalence of Sobolev inequalities and Lieb-Thirring inequalities
• Spectral estimates for two-dimensional Schroedinger operators with application to quantum layers

Cited by in corpus (5)

• Resolvent expansion and time decay of the wave functions for two-dimensional magnetic Schroedinger operators
• A Magnetic Contribution to the Hardy Inequality
• The Hardy inequality and the heat equation with magnetic field in any dimension
• Estimation of the number of negative eigenvalues of magnetic Schrödinger operators in a strip
• Eigenvalue bound for Schroedinger operators with unbounded magnetic field