Generalized Positive-Definite Operator in Quantum Phase Space Obtained by Virtue of the Weyl Quantization Rule
HU Li-Yun1,2, FAN Hong-Yi2
1College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 3300222Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
Generalized Positive-Definite Operator in Quantum Phase Space Obtained by Virtue of the Weyl Quantization Rule
HU Li-Yun1,2, FAN Hong-Yi2
1College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 3300222Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
We introduce a generalized positive-definite operator Δg(q,p) by smoothing out the Wigner operator Δw(q,p) and by averaging over the "coarse graining'' function. The function is then regarded as the classical Weyl correspondence of the operator Δg(q,p); in this way we can easily identify a quantum state |Φ> such that Δg(q,p)=|Φ><Φ|, and |Φ> turns out to be a new kind of squeezed coherent state. Correspondingly, the generalized distribution function for any state |φ> is <φ| Δg(q,p) |φ> =|<Φ|φ>|2 , which is obviously positive-definite and is a generalization of the Husimi function.
We introduce a generalized positive-definite operator Δg(q,p) by smoothing out the Wigner operator Δw(q,p) and by averaging over the "coarse graining'' function. The function is then regarded as the classical Weyl correspondence of the operator Δg(q,p); in this way we can easily identify a quantum state |Φ> such that Δg(q,p)=|Φ><Φ|, and |Φ> turns out to be a new kind of squeezed coherent state. Correspondingly, the generalized distribution function for any state |φ> is <φ| Δg(q,p) |φ> =|<Φ|φ>|2 , which is obviously positive-definite and is a generalization of the Husimi function.
HU Li-Yun;FAN Hong-Yi. Generalized Positive-Definite Operator in Quantum Phase Space Obtained by Virtue of the Weyl Quantization Rule[J]. 中国物理快报, 2009, 26(6): 60307-060307.
HU Li-Yun, FAN Hong-Yi. Generalized Positive-Definite Operator in Quantum Phase Space Obtained by Virtue of the Weyl Quantization Rule. Chin. Phys. Lett., 2009, 26(6): 60307-060307.
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