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.
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|
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