Concise Treatise On Quantum Mechanics In Phase Space, A by Thomas L Curtright | (PDF) Free Download

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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.

User’s Reviews

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⭐This concise version of Quantum Mechanics in Phase Space is a highly readable but rigorous introduction to Wigner’s clever and exact reformulation of quantum mechanics, which allows one to work with position and momentum simultaneously, instead of treating them as mutually exclusive alternatives. (Wave functions in X- or P-space are replaced by a joint distribution over X and P, and operators by garden-variety c-numbers.)The topic should be of interest not just to physicists pondering the Uncertainty Principle, but to electrical engineers concerned with practical applications of time-frequency analysis to signal processing. It may also be of interest in fluid mechanics, specifically to the problem of spatially non-uniform turbulence characterized by a Kolmogorov-like power spectrum modulated by spatial variations in overall intensity.The historical introduction is as interesting as the mathematical discussion. The heroes are Eugene Wigner and two starving graduate students.

⭐Quantum Mechanics (QM) remains a mysterious domain for many. Why work with operators and Hilbert spaces? This treatise, after first presenting a fascinating overview about the lives and ideas of the main players in the field, goes on to introduce a novel ‘third way’ to do stationary and dynamical QM by associating number-functions with observables in ordinary (p,q) space, based on the transforms originally proposed by Von Neumann and Weyl and on Wigner’s quasi-probability function. The authors, being masters in this field, present a wealth of theorems and lemmas for the phase space method, the main new elements being the need of the star product (*) and the Moyal bracket as developed by Groenewold in Holland (1946) and Moyal in Britain (1949). With the phase-space method being fully function-based, it is now the nature of these new products and brackets that harbor the quantum aspects of nature, since they are complex expressions of Planck’s constant h. However, lo and behold – they readily admit the classical limit h => 0, showing classical Liouville flow. This method thus clearly shows the unity of all physics, with quantum and classical physics sharing a common description, the former being, however, the richer one.I would love to give a one-semester course based on this book. There are many exercises that will challenge the students. For those who do not teach: any science lover should have this jewel of a book in his/her bookcase!

⭐This is an excellent treatment of a difficult mathematical topic, which is gaining in importance. It is understandable to physics or engineering graduate students. The historical survey at the beginning is accurate and interesting reading. If this little volume has any faults, it is in the lack pf practical examples of the utility of the new formalism, such as quantum optics, superconductivity, or the quantum Hall effect, none of which are discussed, making the book more of a “coffee table” item. But it is interesting as a stand-alone introduction to its field.

⭐If you search for a pedagogical introduction, or something that helps you introducing the theory, don’t buy this book. This is more of a survey of some concepts. They glued together the overview of the book written some years ago and some history on the scientists involved. The article on Wikipedia on this theme is much more informative than this whole book.I gave two stars and not one because they improved the LateX inside, and because they made some extremely little effort expanding with some new phrases.

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