Agarwal, G. S. ; Wolf, E. (1970) Calculus for functions of noncommuting operators and general phasespace methods in quantum mechanics. II. Quantum mechanics in phase space Physical Review D  Particles, Fields, Gravitation and Cosmology, 2 (10). pp. 21872205. ISSN 15507998

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Official URL: http://prd.aps.org/abstract/PRD/v2/i10/p2187_1
Related URL: http://dx.doi.org/10.1103/PhysRevD.2.2187
Abstract
In Paper I of this investigation a new calculus for functions of noncommuting operators was developed, based on the notion of mapping of operators onto cnumber functions. With the help of this calculus, a general theory is formulated, in the present paper, of phasespace representation of quantummechanical systems. It is shown that there is a whole class of such representations, one associated with each type of mapping, the simplest one being the wellknown representation due to Weyl. For each representation, the quantummechanical expectation value of an operator is found to be expressible in the form of a phasespace average of classical statistical mechanics. The phasespace distribution functions are, however, not true probabilities, in general. The phasespace forms of the main quantummechanical equations of motion are obtained and are found to have the form of a generalized Liouville equation. The phasespace form of the Bloch equation for the density operator of a quantum system in thermal equilibrium is also derived. The generalized characteristic functions of boson systems are defined and their main properties are studied. The equations of motion for the characteristic functions are also derived. As an illustration of the theory, a generalized stochastic description of a quantized electromagnetic field is obtained.
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Deposited On:  23 Jan 2012 14:44 
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