Wigner function for the Dirac oscillator in spinor space

  • The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.
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  • [1] Wigner E. Phys. Rev., 1932, 40: 749-7592 Bertrand J, Bertrand P. Foundat. Phys., 1987, 17: 397-4053 Vogel K, Risken H. Phys. Rev. A, 1989, 40: 2847-28494 Kim Y,Wigner E. Phys. Rev. A, 1987, 36: 1293-1297; 1988, 38: 1159-11675 Hillery M, O'Connell R, Scully M et al. Phys. Repts., 1984, 106(3): 121-1676 Balasz N L, Jennings B K. Phys. Repts., 1984, 104(6): 347-3917 Takayuki Hori, Takao Koikawa, Takuya Maki. Prog. Theor. Phys, 2002, 108: 1123-11418 Lee Hai-Woong. Phys. Repts., 1995, 259(3): 147-2119 Zachos Cosmas. Int. J. Mod. Phys. A, 2002, 17: 297-31610 Nuno Costa Dias, Joao Nuno Prata. J. Math. Phys., 2007, 48: 012109-01212711 Moshinskyt M, Szczepaniaks A. J. Phys. A: Math. Gen., 1989, 22: 817-82012 WANG Jian-Hua, LI Kang. J. Phys. A: Math. Theor., 2007, 40: 2197-220213 Kurtsiefer Ch, Pfau T, Mlynek J. Nature, 1997, 386: 150-15314 HENG Tai-Hua, LIN Bing-Sheng, JING Si-Cong. Chin. Phys. Lett., 2008, 25: 3535-353815 WANG Jian-Hua, Li Kang. Chin. Phys. Lett., 2007, 24: 5-716 HENG Tai-Hua, LI Ping, JING Si-Cong. Chin. Phys. Lett., 2007, 24: 592-59517 DULAT Sayipjamal, LI Kang. Chin. Phys. C, 2008, 32: 92-9518 DULAT Sayipjamal, LI Kang. Eur. Phys. J. C, 2008, 54: 333-33719 LI Kang, WANG Jian-Hua. Eur. Phys. J. C, 2007, 50(4): 1007-101120 LI Kang, WANG Jian-Hua, CHEN Chi-Yi. Mod. Phys. Lett. A, 2005, 20(28): 2165-217421 LI Kang, DULAT Sayipjamal. Eur. Phys. J. C, 2006, 46: 825-82822 LI Kang, WANG Jian-Hua, DULAT Sayipjamal et al. Int. J. Theor. Phys., 2010, 49: 134-143
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MA Kai, WANG Jian-Hua and YUAN Yi. Wigner function for the Dirac oscillator in spinor space[J]. Chinese Physics C, 2011, 35(1): 11-15. doi: 10.1088/1674-1137/35/1/003
MA Kai, WANG Jian-Hua and YUAN Yi. Wigner function for the Dirac oscillator in spinor space[J]. Chinese Physics C, 2011, 35(1): 11-15.  doi: 10.1088/1674-1137/35/1/003 shu
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Received: 2010-03-01
Revised: 2010-04-08
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Wigner function for the Dirac oscillator in spinor space

Abstract: The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.

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