Non-self-adjoint Schrödinger Operator with a Periodic Potential

Focusing on the spectral analysis of non-self-adjoint Schrödinger operators, this book explores the spectrum and spectral singularities of periodic complex-valued potentials. It delves into the Mathieu-Schrödinger operator and the Schrödinger operator with parity-time (PT)-symmetric potentials, addressing the lack of a general spectral theorem for non-self-adjoint operators. With detailed proofs and a thorough approach, it serves as a valuable resource for graduate students in physics and mathematics, paving the way for advancements in non-Hermitian quantum mechanics and optics.