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 a 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.57 TABLE III. Dependence of the absolute errors (times 10~ 12) of the Wigner function approximation Eq. (13) of the ... approximation to the exact solution we evaluate our spectral solution on an equidistant grid consisting of 100X100 points.

Title | : | Quantum Mechanics in Phase Space |

Author | : | Cosmas Zachos, David Fairlie, Thomas Curtright |

Publisher | : | World Scientific - 2005-01-01 |

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