Recent Mathematical and Theoretical Progress in Quantum Mechanics

C. Piron

Tosio Kato

Tosio Kato; Some Mathematical Problems in Quantum Mechanics, Progress of Theoretical Physics Supplement, Volume 40, 1 February 1967, Pages 3–19, https://doi.org

Anne Boutet de Monvel, P. Dita, G. Nenciu +1 more

Fabio Bagarello, Jean‐Pierre Gazeau, Franciszek Hugon Szafraniec +1 more

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 recent emergence of the 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 of 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 pertubation 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, 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.

Roger Schlafly

Much of modern theoretical physics assumes that the true nature of reality is mathematics. This is a great mistake. The assumption underlies most of the paradoxes of quantum mechanics, and has no empirical justification. Accepting that the assumption is wrong will allow physics and mathematics to progress as distinct disciplines.

E. U. Condon