Non-self-adjoint Schrödinger Operator with a Periodic Potential

Focusing on the spectral analysis of non-self-adjoint Schrödinger operators, this book explores complex-valued periodic potentials and spectral singularities. It includes a thorough examination of the Mathieu-Schrödinger operator and the Schrödinger operator with parity-time (PT)-symmetric periodic optical potential. By addressing the lack of a general spectral theorem for non-self-adjoint operators, the work presents innovative approaches that enhance understanding in non-Hermitian quantum mechanics and optics, making it ideal for graduate students in physics and mathematics.