Schrödinger Operators with Many Bound States

Abstract

Consider the Schrödinger operators $H_{\pm }=-d^2/d{x}^2\pm V(x)$. We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and several sharp results concerning the spectral properties of $H_{\pm }$.

22 pages

References in corpus (1)

• Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line

Cited by in corpus (3)

• Schroedinger Operators With Few Bound States
• Bound States of Discrete Schroedinger Operators with Super-Critical Inverse Square Potentials
• Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators