A Concise Treatise On Quantum Mechanics In Phase Space
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| Author | : Thomas L Curtright |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 170 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 9814520462 |
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions — density matrices in a special Weyl representation — and star products are the cornerstones of the formalism.The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject.In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products.This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.
| Author | : Thomas Curtright |
| Publisher | : World Scientific Publishing Company Incorporated |
| Total Pages | : 159 |
| Release | : 2014 |
| Genre | : Science |
| ISBN | : 9789814520430 |
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density matrices in a special Weyl representation and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase-space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products. This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.
| Author | : Thomas L. Curtright |
| Publisher | : |
| Total Pages | : 170 |
| Release | : 2013 |
| Genre | : Electronic books |
| ISBN | : 9789814520454 |
| Author | : Cosmas Zachos |
| Publisher | : World Scientific |
| Total Pages | : 560 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812383840 |
Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics.
| Author | : Ademir E. Santana |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 294 |
| Release | : 2023-12-21 |
| Genre | : Science |
| ISBN | : 1527556433 |
The present monograph brings to readers, as researchers and students of physics and mathematics, recent developments in symmetries, where the representation space is a symplectic manifold. This gives rise to the quantum field theory formulated in through the concept of phase space and associated with the Wigner function, a quasi-distribution of probability. This approach provides information about non-classicality of quantum systems, describes quantum chaos and is the starting point of the quantum kinetic theory. In this realm, abelian and non-abelian gauge symmetries are introduced with the concept of quasi-amplitude of probability. This leads, for instance, to Symplectic Schrödinger, Klein-Gordon and Dirac equations dealing with systems in condensed matter and particle physics. These achievements are depicted here, following a pedagogical model of presentation.
| Author | : Marcos Mariño |
| Publisher | : Cambridge University Press |
| Total Pages | : 273 |
| Release | : 2021-12-09 |
| Genre | : Science |
| ISBN | : 1108495877 |
An advanced quantum mechanics textbook that provides a unique pedagogical introduction to high-level topics in the field.
| Author | : Sergio Cecotti |
| Publisher | : Springer Nature |
| Total Pages | : 846 |
| Release | : 2023-11-07 |
| Genre | : Science |
| ISBN | : 3031365305 |
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
| Author | : Dieter Meschede |
| Publisher | : Springer |
| Total Pages | : 799 |
| Release | : 2018-01-02 |
| Genre | : Science |
| ISBN | : 3319643460 |
This edition contains carefully selected contributions by leading scientists in high-resolution laser spectroscopy, quantum optics and laser physics. Emphasis is given to ultrafast laser phenomena, implementations of frequency combs, precision spectroscopy and high resolution metrology. Furthermore, applications of the fundamentals of quantum mechanics are widely covered. This book is dedicated to Nobel prize winner Theodor W. Hänsch on the occasion of his 75th birthday. The contributions are reprinted from a topical collection published in Applied Physics B, 2016. Selected contributions are available open access under a CC BY 4.0 license via link.springer.com. Please see the copyright page for further details.
| Author | : Stuart A. Rice |
| Publisher | : John Wiley & Sons |
| Total Pages | : 574 |
| Release | : 2016-08-29 |
| Genre | : Science |
| ISBN | : 1119290945 |
The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. • This is the only series of volumes available that presents the cutting edge of research in chemical physics. • Includes contributions from experts in this field of research. • Contains a representative cross-section of research that questions established thinking on chemical solutions • Structured with an editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry or chemical physics
| Author | : James H. Luscombe |
| Publisher | : CRC Press |
| Total Pages | : 257 |
| Release | : 2024-09-23 |
| Genre | : Science |
| ISBN | : 1040118798 |
Statistical mechanics provides a framework for relating the properties of macroscopic systems (large collections of atoms, such as in a solid) to the microscopic properties of its parts. However, what happens when macroscopic systems are not in thermal equilibrium, where time is not only a relevant variable, but also essential? That is the province of nonequilibrium statistical mechanics – there are many ways for systems to be out of equilibrium! The subject is governed by fewer general principles than equilibrium statistical mechanics and consists of a number of different approaches for describing nonequilibrium systems. Financial markets are analyzed using methods of nonequilibrium statistical physics, such as the Fokker-Planck equation. Any system of sufficient complexity can be analyzed using the methods of nonequilibrium statistical mechanics. The Boltzmann equation is used frequently in the analysis of systems out of thermal equilibrium, from electron transport in semiconductors to modeling the early Universe following the Big Bang. This book provides an accessible yet very thorough introduction to nonequilibrium statistical mechanics, building on the author's years of teaching experience. Covering a broad range of advanced, extension topics, it can be used to support advanced courses on statistical mechanics, or as a supplementary text for core courses in this field. Key Features: Features a clear, accessible writing style which enables the author to take a sophisticated approach to the subject, but in a way that is suitable for advanced undergraduate students and above Presents foundations of probability theory and stochastic processes and treats principles and basic methods of kinetic theory and time correlation functions Accompanied by separate volumes on thermodynamics and equilibrium statistical mechanics, which can be used in conjunction with this book
