Non-self-adjoint Schrödinger operator with a periodic potential
著者
書誌事項
Non-self-adjoint Schrödinger operator with a periodic potential
Springer, c2021
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This book gives a complete spectral analysis of the non-self-adjoint Schroedinger 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 Schroedinger operator, the book features a complete spectral analysis of the Mathieu-Schroedinger operator and the Schroedinger 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.
目次
1. Spectral Theory for the Schroedinger Operator with a Complex-Valued Periodic Potential.- 2. On the Special Potentials.- 3. On the Matheiu-Schroedinger Operator.- 4. PT-Symmetric Periodic Optical Potential.- Index.
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