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In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1/exp[2i(q-Q)(p-P)], here denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules(P-Q ordering, Q-P ordering and Weyl ordering). We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained.
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Keywords:
- commutative relation /
- integral transformation /
- Weyl ordering /
- Wigner function
[1] Dragoman D 2002 Progress In Optics 42 424
[2] Dragoman D, Dragoman M 1999 Prog. Quantum Electron. 23 131
[3] Crasser O, Mack H, Schleich W P 2004 Fluct. Noise Lett. 04 L43
[4] Nienhuis G, Allen L 1993 Phys. Rev. A 48 656
[5] Wolf K B and Kurmyshev E V 1993 Phys. Rev. A 47 3365
[6] Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[7] L C H, Fan H Y, Jiang N Q 2010 Chin. Phys. B 19 120303
[8] Fan H Y 2003 Phys. Lett. A 313 343
[9] Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 014204
[10] Weyl H 1927 Z. Phys. 46 1
[11] Wigner E 1932 Phys. Rev. 40 749
[12] Wang J S, Fan H Y, Meng X G 2012 Chin. Phys. B 21 064204
[13] Fan H Y 1992 J. Phys. A 25 3443
[14] Fan H Y 1997 Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics—Progress of Dirac's Symbolic Method (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [范洪义1997 量子力学表象与变换论-狄拉克符号法进展(上海: 上海科技出版社)
[15] Fan H Y 2008 Commun. Theor. Phys. 50 935
[16] Fan H Y 2013 Acta Phys. Sin. 62 020302 (in Chinese) [范洪义 2013 62 020302]
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[1] Dragoman D 2002 Progress In Optics 42 424
[2] Dragoman D, Dragoman M 1999 Prog. Quantum Electron. 23 131
[3] Crasser O, Mack H, Schleich W P 2004 Fluct. Noise Lett. 04 L43
[4] Nienhuis G, Allen L 1993 Phys. Rev. A 48 656
[5] Wolf K B and Kurmyshev E V 1993 Phys. Rev. A 47 3365
[6] Dirac P A M 1930 The Principle of Quantum Mechanics (Oxford: Clarendon Press)
[7] L C H, Fan H Y, Jiang N Q 2010 Chin. Phys. B 19 120303
[8] Fan H Y 2003 Phys. Lett. A 313 343
[9] Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 014204
[10] Weyl H 1927 Z. Phys. 46 1
[11] Wigner E 1932 Phys. Rev. 40 749
[12] Wang J S, Fan H Y, Meng X G 2012 Chin. Phys. B 21 064204
[13] Fan H Y 1992 J. Phys. A 25 3443
[14] Fan H Y 1997 Fan H Y 1997 Representation and Transformation Theory in Quantum Mechanics—Progress of Dirac's Symbolic Method (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [范洪义1997 量子力学表象与变换论-狄拉克符号法进展(上海: 上海科技出版社)
[15] Fan H Y 2008 Commun. Theor. Phys. 50 935
[16] Fan H Y 2013 Acta Phys. Sin. 62 020302 (in Chinese) [范洪义 2013 62 020302]
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