Journal of Quantum Optics, Volume. 30, Issue 1, 10103(2024)

Two Basic Operator Identities in Quantum Optics Obtained by Virtue of the Two-Variable Hermite Polynomials

ZHAN De-hui1、* and FAN Hong-yi2
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
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    References(11)

    [1] [1] SCULLY M O, ZUBAIRY M S. Quantum optics[M]. UK: Cambridge University Press, 1997.

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    [3] [3] BIN-SAAD M G. Modified 2D-complex Hermite polynomials: Their quasi-monomiality and operational identities[J]. Journal of Mathematical Analysis and Applications, 2023, 524(1):127066. DOI: 10.1016/j.jmaa.2023.127066.

    [4] [4] ZHANG K, LI L L, YU P P, et al. Quantum entangled fractional Fourier transformbased on the IWOP technique[J]. Chinese Physics B, 2023, 32(4):040302. DOI: 10.1088/1674-1056/ac7e32.

    [5] [5] FAN H Y, YUAN H C. From coherent state to compressed state[M]. Hefei: University of Science and Technology of China Press, 2012. (in Chinese).

    [6] [6] FAN H Y, TANG X B. Advances in the mathematical foundations of quantum mechanics[M]. Hefei: University of Science and Technology of China Press, 2008. (in Chinese).

    [7] [7] ESRA E D, HAKAN C. A new family of two-variable polynomials based on hermite polynomials[J]. Mathematica Slovaca, 2022, 72(4):885-898. DOI: 10.1515/ms-2022-0060.

    [8] [8] FAN H Y. Representation and transformation theory in quantum mechanics[M]. Shanghai: Shanghai Science and Technology Press, 1997:43-44. (in Chinese).

    [9] [9] FAN H Y, WENG H G. Simple approach for deriving the Weyl correspondence product formula[J]. Communications in Theoretical Physics, 1992, 18(3):343-346. DOI: 10.1088/0253-6102/18/3/343.

    [10] [10] FAN H Y, ZAIDI H R. Application of IWOP technique to the generalized Weyl correspondence[J]. Physics Letters A, 1987, 124(6-7):303-307. DOI: 10.1016/0375-9601(87)90016-8.

    [11] [11] LIANG K M. Methods of Mathematical Physics: 3rd ed[M]. Beijing: Higher Education Press, 1998. (in Chinese).

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    ZHAN De-hui, FAN Hong-yi. Two Basic Operator Identities in Quantum Optics Obtained by Virtue of the Two-Variable Hermite Polynomials[J]. Journal of Quantum Optics, 2024, 30(1): 10103

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    Paper Information

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    Received: Dec. 22, 2023

    Accepted: --

    Published Online: Aug. 23, 2024

    The Author Email: ZHAN De-hui (dhzhan@mail.ustc.edu.cn)

    DOI:10.3788/jqo20243001.0103

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