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
[1] [1] SCULLY M O, ZUBAIRY M S. Quantum optics[M]. UK: Cambridge University Press, 1997.
[2] [2] ZENG J Y. Quantum Mechanics: 3rd ed. Volume I[M]. Beijing: Science Press, 2000. (in Chinese).
[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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Received: Dec. 22, 2023
Accepted: --
Published Online: Aug. 23, 2024
The Author Email: ZHAN De-hui (dhzhan@mail.ustc.edu.cn)