This book gives a complete spectral analysis of the
non-self-adjoint Schroedinger 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 Schroedinger operator,
the book features a complete spectral analysis of the
Mathieu-Schroedinger operator and the Schroedinger 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.
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