PT-Symmetric Schrödinger Operators with Unbounded Potentials

Jan Nesemann

ISBN 10: 3834817627 / ISBN 13: 9783834817624

Published by Vieweg+Teubner Verlag, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783834817624

Bibliographic Details

• Title: PT-Symmetric Schrödinger Operators with Unbounded Potentials
• Publisher: Vieweg+Teubner Verlag
• Publication Date: 2011
• Language: English
• ISBN 10: 3834817627
• ISBN 13: 9783834817624
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 210W x 148H x 7D millimeters 210 millimeters width by 148 millimeters height by 7 millimeters depth
• Weight: 146 grams

About this title

Synopsis

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.