Non-self-adjoint Schrödinger Operator with a Periodic Potential
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Beschreibung
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.
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.
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
Autor*in
Oktay Veliev
Themen in »Non-self-adjoint Schrödinger Operator with a Periodic Potential«
Non-self-adjoint Operators Schrödinger Operators Periodic Differential Operators PT-symmetric Potentials Periodic Optical Potential Spectral Analysis of the Schrödinger Operator Mathieu-Hill Operator Spectral Expansion of the Hill Operator Matheiu-Schrödinger Operator