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Gaussian-Wigner distributions in quantum mechanics and optics

Simon, R and Sudarshan, ECG and Mukunda, N (1987) Gaussian-Wigner distributions in quantum mechanics and optics. In: Physical Review A., 36 (8). pp. 3868-3880.

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Abstract

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: Journal Article
Additional Information: The copyright of this article belongs to The American Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Date Deposited: 26 Jul 2004
Last Modified: 19 Sep 2010 04:13
URI: http://eprints.iisc.ernet.in/id/eprint/973

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