By Thomas L Curtright, David B Fairlie, Cosmas K Zachos
Wigner's quasi-probability distribution functionality in part house is a distinct (Weyl) illustration of the density matrix. it's been priceless in describing quantum shipping in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. it's also very important in sign processing and the math of algebraic deformation. A striking point of its inner good judgment, pioneered via Groenewold and Moyal, has in simple terms emerged within the final quarter-century: it furnishes a 3rd, substitute, formula of quantum mechanics, self sustaining of the traditional Hilbert area, or course essential formulations.
In this logically entire and self-standing formula, one don't need to decide on facets - coordinate or momentum area. it really works in complete section house, accommodating the uncertainty precept, and it deals specified insights into the classical restrict of quantum conception. This precious e-book is a suite of the seminal papers at the formula, with an introductory evaluate which gives a path map for these papers; an in depth bibliography; and easy illustrations, compatible for purposes to a extensive variety of physics difficulties. it may offer supplementary fabric for a starting graduate path in quantum mechanics.
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Post 12 months word: First released July 1st 1980
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Additional resources for Quantum Mechanics in Phase Space
Such quantum effects have been observed for physical quantities such as resistance, magnetic flux, vortex line and voltage, etc. The macroscopic quantum effect is obviously different from the microscopic quantum effect in which physical quantities depicting microscopic particles, such as energy, momentum and angular momentum, are quantized. Thus it is reasonable to believe that the fundamental nature and the rules governing these effects are different. We know that the microscopic quantum effect is described by the LQM theory.
Thus it is reasonable to believe that the fundamental nature and the rules governing these effects are different. We know that the microscopic quantum effect is described by the LQM theory. But what are the mechanisms for the macroscopic quantum effects? How can these effects be properly described? These questions apparently need to be addressed. We all know that materials are composed of a great number of microscopic particles such as atoms, electrons, nuclei and so on, which exhibit quantum features.
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