Download Non-Self-Adjoint Schrodinger Operator with a Periodic Potential 2nd Edition
This book presents an in-depth study of spectral theory for non-self-adjoint differential operators with complex periodic coefficients, focusing on one of the most difficult challenges in modern mathematical physics and quantum theory: developing spectral decompositions without relying on a general spectral theorem. It explores a broad range of operators, from scalar and vector Schrödinger equations to PT-symmetric periodic optical systems and extends the discussion to higher-order differential operators with periodic matrix-valued coefficients.
The Non-Self-Adjoint Schrödinger Operator with a Periodic Potential: Spectral Theories for Scalar and Vectorial Cases and Their Generalizations introduces substantial improvements and includes two additional chapters that provide a more complete and unified treatment of non-self-adjoint periodic operators. One new chapter investigates vector Schrödinger operators with matrix potentials, presenting detailed results on their spectra, eigenvalues, eigenfunctions, and spectral expansions. The other develops a general framework for ordinary differential operators of arbitrary order with periodic coefficients, including vector-valued cases and a full classification of spectra for PT-symmetric periodic operators. These additions make this edition one of the most extensive references available on the subject.
Starting from the fundamental concepts of spectral analysis for Schrodinger operators with complex periodic potentials, the book gradually moves toward advanced topics such as the Mathieu–Schrödinger operator and PT-symmetric periodic structures. Through a systematic and accessible approach, it serves as a valuable resource for graduate students, mathematicians, physicists, and researchers interested in spectral theory, quantum mechanics, optics, and mathematical physics.
- Author (s): Oktay Veliev
- Year of publication: 2025
- Publisher: Springer
- Language: English
- ISBN: 3031902580, 9783031902581, 9783031902598
- Number of pages: 481 pages
- Book format: PDF
- File size: 4.40 MB
