Gaussian-Wigner distributions in quantum mechanics and optics

Simon, R. ; Sudarshan, E. C. G. ; Mukunda, N. (1987) Gaussian-Wigner distributions in quantum mechanics and optics Physical Review A, 36 (8). pp. 3868-3880. ISSN 1050-2947

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Gaussian kernels representing operators on the Hilbert space scrH=L2(openRn) are studied. Necessary and sufficient conditions on such a kernel in order that the corresponding operator be positive semidefinite, corresponding to a density matrix (cross-spectral density) in quantum mechanics (optics), are derived. The Wigner distribution method is shown to be a convenient framework for characterizing Gaussian kernels and their unitary evolution under Sp(2n,openR) action. The nontrivial role played by a phase term in the kernel is brought out. The entire analysis is presented in a form which is directly applicable to n-dimensional oscillator systems in quantum mechanics and to Gaussian Schell-model partially coherent fields in optics.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:25292
Deposited On:06 Dec 2010 13:37
Last Modified:17 May 2016 08:47

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