Non-self-adjoint Schrödinger Operator with a Periodic Potential
Springer International Publishing (Verlag)
978-3-030-72682-9 (ISBN)
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.
Oktay Veliev received his B.S. degree in Mathematics in 1977 and Ph.D. degree in Mathematics in 1980 from Moscow State University, earning a Doctor of Sciences degree in 1989. From 1980 to 1983, he was a researcher and then a senior researcher (1983-1988) at the Institute of Mathematics of the Academy of Sciences of Azerbaijan SSR. At Baku State University (Azerbaijan), he has been Associate Professor (1988-1991), Professor (1991-1992), and Head of the Department of Functional Analysis (1992-1997). Between 1993 and 1997, he was President of the Azerbaijan Mathematical Society. He was Visiting Professor at the University of Nantes (France), the Institute of Mathematics at the ETH (Switzerland), and Sussex University (England). From 1997 to 2002, he was Professor at Dokuz Eylul University (Turkey) and since 2003 has been Professor at Dogus University (Turkey). He has received grants from the American Mathematical Society and the International Science Foundation (Grant No. MVVOOO).
1. Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential.- 2. On the Special Potentials.- 3. On the Matheiu-Schrödinger Operator.- 4. PT-Symmetric Periodic Optical Potential.- Index.
| Erscheinungsdatum | 22.06.2021 |
|---|---|
| Zusatzinfo | X, 294 p. 10 illus., 9 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 578 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | Matheiu-Schrödinger Operator • Mathieu-Hill Operator • Non-self-adjoint Operators • Periodic Differential Operators • Periodic Optical Potential • PT-symmetric Potentials • Schrödinger Operators • Spectral Analysis of the Schrödinger Operator • Spectral Expansion of the Hill Operator |
| ISBN-10 | 3-030-72682-7 / 3030726827 |
| ISBN-13 | 978-3-030-72682-9 / 9783030726829 |
| Zustand | Neuware |
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