Trace formulas for Schrödinger operators with complex potentials on a half line

Research output

Abstract

We consider Schrödinger operators with complex-valued decaying potentials on the half line. Such operator has essential spectrum on the half line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half line. We determine trace formula: sum of imaginary part of these eigenvalues plus some singular measure plus some integral from the Jost function. Moreover, we estimate sum of imaginary part of eigenvalues and singular measure in terms of the norm of potentials. In addition, we get bounds on the total number of eigenvalues, when the potential is compactly supported.

Original languageEnglish
Pages (from-to)1-20
JournalLetters in Mathematical Physics
Volume110
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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