Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics
FAN Hong-Yi1,2, Li Hong-Qi1
1Department of Physics, Heze University, Heze 2740152Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics
FAN Hong-Yi1,2;Li Hong-Qi1
1Department of Physics, Heze University, Heze 2740152Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
摘要Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states (such as the coordinate eigenstate, the momentum eigenstate and the coherent state) into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.
Abstract：Based on the technique of integration within an ordered product of operators we investigate a completeness relation of pure states (such as the coordinate eigenstate, the momentum eigenstate and the coherent state) into normally ordered Gaussian forms. The Weyl ordering invariance under similarity transformations is employed to reveal physical meaning of a kind of normally ordered Gaussian operators, which have the similar forms to the bivariate normal distributions in statistics, i.e., the thermo mixed state density matrix.
FAN Hong-Yi;Li Hong-Qi. Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics[J]. 中国物理快报, 2007, 24(12): 3322-3324.
FAN Hong-Yi, Li Hong-Qi. Physics of a Kind of Normally Ordered Gaussian Operators in Quantum Optics. Chin. Phys. Lett., 2007, 24(12): 3322-3324.
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2007, Vol. 24 
