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PT-Symmetric Schrödinger Operators with Unbounded Potentials

  • Book
  • © 2011

Overview

Authors:
  1. Jan Nesemann
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Table of contents (4 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Jan Nesemann
    Pages 1-7

  3. Relatively Bounded Perturbations in Krein Spaces

    • Jan Nesemann
    Pages 9-34

  4. Relatively Form-Bounded Perturbations in Krein Spaces

    • Jan Nesemann
    Pages 35-64

  5. Examples

    • Jan Nesemann
    Pages 65-77

  6. Back Matter

    Pages 79-83
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Keywords

About this book

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.

About the author

Dr. Jan Nesemann holds a master’s degree in mathematics as well as in business administration. He received his PhD in mathematics from the University of Bern under the guidance of Prof. Dr. Christiane Tretter. Currently he works as an actuarial and financial services consultant in Zurich.

Bibliographic Information

  • Book Title: PT-Symmetric Schrödinger Operators with Unbounded Potentials

  • Authors: Jan Nesemann

  • DOI: https://doi.org/10.1007/978-3-8348-8327-8

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2011

  • Softcover ISBN: 978-3-8348-1762-4Published: 14 July 2011

  • eBook ISBN: 978-3-8348-8327-8Published: 14 July 2011

  • Edition Number: 1

  • Number of Pages: VIII, 83

  • Topics: Operator Theory, Mathematics, general

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