中国物理B ›› 2010, Vol. 19 ›› Issue (6): 64207-064207.doi: 10.1088/1674-1056/19/6/064207
A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation
范洪义1, 完绍龙2, 谢传梅3
- (1)Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; (2)Institute for Theoretical Physics and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; (3)Institute for Theoretical Physics and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;College of Physics and Material Science, Anhui University, Hefei 230039, China
A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation
Xie Chuan-Mei(谢传梅)a)c)†ger, Fan Hong-Yi(范洪义)b), and Wan Shao-Long(完绍龙) a)
- a Institute for Theoretical Physics and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; c College of Physics and Material Science, Anhui University, Hefei 230039, China
摘要： Based on the displacement-squeezing related squeezed coherent state representation ≤ft\vert z\right\rangle _{g} and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens--Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz-rz^{\ast } in the % ≤ft\vert z\right\rangle _{g} representation, while ≤ft\vert z\right\rangle _{g} in phase space is graphically denoted by an ellipse.
中图分类号: (Quantum state engineering and measurements)
- 42.50.Dv