Overview
Solves the problem of the non-self-adjoint Schrödinger operator with periodic potential complete with construction of the spectral expansion
Presents the complete spectral theory of the non-self-adjoint Mathieu-Schrödinger operator
Features a detailed classification of the spectrum and spectral expansion of the Schrödinger operator with a PT-symmetric periodic optical potential
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Table of contents (5 chapters)
Keywords
About this book
This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Non-self-adjoint Schrödinger Operator with a Periodic Potential
Authors: Oktay Veliev
DOI: https://doi.org/10.1007/978-3-030-72683-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-72682-9Published: 20 June 2021
Softcover ISBN: 978-3-030-72685-0Published: 21 June 2022
eBook ISBN: 978-3-030-72683-6Published: 19 June 2021
Edition Number: 1
Number of Pages: X, 294
Number of Illustrations: 1 b/w illustrations, 9 illustrations in colour
Topics: Theoretical, Mathematical and Computational Physics, Quantum Physics, Mathematical Methods in Physics, Condensed Matter Physics, Optics, Lasers, Photonics, Optical Devices