Jean-Pierre Gazeau

Fabio Bagarello

Franciszek Hugon Szafraniec

Miloslav Znojil

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.

Mathematical Aspects

Non-Selfadjoint Operators in Quantum Physics

Introduces number operators with a focus on the relationshipbetween quantum mechanics and social science Mathematics is increasingly applied to classical problems infinance, biology, economics, and elsewhere. Quantum Dynamics forClassical Systems describes how quantum tools—the numberoperator in particular—can be used to create dynamicalsystems in which the variables are operator-valued functions andwhose results explain the presented model. The book presentsmathematical results and their applications to concrete systems anddiscusses the methods used, results obtained, and techniquesdeveloped for the proofs of the results. The central ideas of number operators are illuminated whileavoiding excessive technicalities that are unnecessary forunderstanding and learning the various mathematical applications.The presented dynamical systems address a variety of contexts andoffer clear analyses and explanations of concluded results.Additional features in Quantum Dynamics for ClassicalSystems include: Applications across diverse fields including stock markets andpopulation migration as well as a unique quantum perspective onthese classes of models Illustrations of the use of creation and annihilation operatorsfor classical problems Examples of the recent increase in research and literature onthe many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers whileshedding light on new approaches in the field Quantum Dynamics for Classical Systems is an idealreference for researchers, professionals, and academics in appliedmathematics, economics, physics, biology, and sociology. The bookis also excellent for courses in dynamical systems, quantummechanics, and mathematical models.

Fabio Bagarello

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