Non-self-adjoint Schr’dinger Operator with a Periodic PotentialThis book gives a complete spectral analysis of the non-self-adjoint Schr’dinger 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 Schr’dinger operator, the book features a complete spectral analysis of the Mathieu-Schr’dinger operator and the Schr’dinger 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. ISBN: 9783030726829, 3030726827
