Non-Selfadjoint Operators in Quantum Physics

A unique discussion of mathematical methods with applications to quantum mechanics

Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features:

• Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area
• An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory
• Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics

An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

Fabio Bagarello, PhD, is Professor in the Department of Energy, Information Engineering, and Mathematical Models at the University of Palermo, Italy. Dr. Bagarello is the author of over 160 journal articles and Quantum Dynamics for Classical Systems: With Applications of the Number Operator, also published by Wiley.

Jean Pierre Gazeau, PhD, is Emeritus Professor of Physics in the Laboratory of Astroparticles and Cosmology at the University Paris Diderot, France.  Dr. Gazeau is the author of over 200 journal articles and two books, including Coherent States in Quantum Physics, also published by Wiley.

Franciszek Hugon Szafraniec, Prof. Dr hab., is a retired professor from the Jagiellonian University in Kraków, Poland. He remains an active researcher in functional analysis, and his research interests include operator theory, harmonic analysis, complex function theory, and mathematical foundations of quantum physics. Dr. Szafraniec is also an authority on reproducing kernel Hilbert spaces.

Miloslav Znojil, DrSc, is Leading Research Worker at the Nuclear Physics Institute of the Czech Academy of Sciences and the Deputy Director of the Doppler Institute for Mathematical Physics and Applied Mathematics in the Czech Republic. Dr. Znojil is the author of over 300 journal articles and a member of the Czech Union of Mathematicians and Physicists.