Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.

‘… Professor Nimrod Moiseyev, one of the pioneers in [the] field, does a beautiful job detailing the mathematical underpinnings and describing a myriad of applications ranging from atomic and molecular physics, molecular spectroscopy, chemical reaction dynamics, and electromagnetic wave propagation. Throughout … one finds numerous exercises whose solutions (also provided in good detail) offer the reader much additional insight into both the mathematical intricacies of non-Hermitian quantum theory and its connections to experimental laboratory observations. At the end of each chapter, Moiseyev provides further reading references organized to make connections to the topics covered in the respective chapter and includes references from very diverse sciences. Seldom does one find a book that can be used as a student text for a graduate-level class and that treats its topic at a cutting-edge research level. Professor Moiseyev has produced such a gem in this case!’

Jack Simons - University of Utah

'A unique, timely and comprehensive collection of material relating to the quantum physics and chemistry of resonance and absorption, combining mathematical principles, numerics, applications and solved exercises, representing a lifetime of research by the author and his collaborators.'

Michael Berry - University of Bristol