Estimates of eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials

TL;DR

This paper derives bounds for the eigenvalues of Schrödinger operators on the half-line with complex potentials, extending previous results to include potentials in weak Lebesgue classes, thereby broadening the understanding of spectral properties.

Contribution

It provides new eigenvalue estimates for Schrödinger operators with complex potentials, including those in weak Lebesgue classes, generalizing earlier work by Frank, Laptev, and Seiringer.

Findings

Eigenvalue estimates for complex-valued potentials

Extension to weak Lebesgue class potentials

Generalization of previous spectral bounds

Abstract

Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover those known previously due to R. L. Frank, A. Laptev and R. Seiringer [In spectral theory and analysis, vol. 214, Oper. Theory Adv. Appl., pag. 39-44; Birkh\"{a}user/Springer Basel.]