PT-symmetric Schrödinger operators with unbounded potentials

Resource Information

The work PT-symmetric Schrödinger operators with unbounded potentials represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

PT-symmetric Schrödinger operators with unbounded potentials

Statement of responsibility

Jan Nesemann

Creator

• Nesemann, Jan

Subject

• Kreĭn spaces
• Kreĭn spaces
• Kreĭn spaces
• Operator theory
• Operator theory
• Operator theory

Language

eng

Summary

Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all - provided one is familiar with the theory of self-adjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum

Cataloging source

HKP

Dewey number

510

Index

no index present

Language note

English

LC call number

QA329

LC item number

.N47 2011eb

Literary form

non fiction

Nature of contents

dictionaries