Fock-Space Projector Studied in Weyl Ordering Approach |
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| Authors: | Zhi-song Yu Gui-hua Ren Hong-yi Fan Gen-Chang Cai and Nian-Quan Jiang |
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| Institution: | (1) College of Physics and Electronic Science, Hubei Normal University, Huangshi, Hubei, 435002, China;(2) School of Mechanic and Electric Engineering, Huangshi Institute of Technology, Huangshi, Hubei, 435003, China;(3) Department of Physics, Shanghai Jiao Tong University, Shanghai, 200030, China;(4) College of Music, Wenzhou University, Wenzhou, 325035, China;(5) College of Physics and Electric Information, Wenzhou University, Wenzhou, 325035, China; |
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| Abstract: | We find that the Fock space projector |n〉〈n| is a Weyl ordered Laguerre polynomial 2 ::(-)nLn ( 4afa ) e-2afa ::2{\,}^{:}_{:}(-)^{n}L_{n} ( 4a^{\dagger}a ) e^{-2a^{\dagger}a}{\,}^{:}_{:}, where a † a is the number operator,:: ::,{}^{:}_{:}\ {}^{:}_{:} denotes the Weyl ordering symbol. This brings convenience to derive the Wigner functions of many other quantum states. |
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