中国物理B ›› 2010, Vol. 19 ›› Issue (6): 64207-064207.doi: 10.1088/1674-1056/19/6/064207

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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. (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
  • 收稿日期:2009-11-19 出版日期:2010-06-15 发布日期:2010-06-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10874174 and 10675108), the President Foundation of the Chinese Academy of Sciences, and the Specilized Research Fund for the Doctorial Program of the Higher Education of Ch

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)   

  1. 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
  • Received:2009-11-19 Online:2010-06-15 Published:2010-06-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~10874174 and 10675108), the President Foundation of the Chinese Academy of Sciences, and the Specilized Research Fund for the Doctorial Program of the Higher Education of Ch

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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.

Abstract: Based on the displacement-squeezing related squeezed coherent state representation $|z\rangle _{g}$ 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 $|z\rangle _{g}$ representation, while $|z\rangle _{g}$ in phase space is graphically denoted by an ellipse.

Key words: generalized Fresnel operator, generalized Collins formula, phase space, IWOP technique, squeezed coherent state

中图分类号:  (Quantum state engineering and measurements)

  • 42.50.Dv