Path Integral of the Angular Momentum Eigenstates Evolving Whitthe Parameter Linked With Rotation Angle Under the Space Rotation Transformation

  • We study the method which directly adopts the azimuthal angles and the rotation angle of the axis to describe the evolving process of the angular momentum eigenstates under the space rotation transformation we obtain the angular momentum rotation and multi-rotation matrix elements ' path integral which evolves with the parameter λ(0→θ,θ the rotation angle), and establish the general method of treating the functional (path) integral as a normal multi-integrals.
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  • [1] Feynman R P, Hibbs A R Quantum Mechanics and Path Integrals. New York: Mcgraw-Hill Press, 1965. 21-43[2] Abers E S, Lee B W. Phys. Rep. C, 1973, 9 (1): 1-141[3] de Witt-Morette C, Maheshwari A, Nelson B. Phys. Rep. C, 1979, 50(5): 255-372[4] Marinov M S. Phys. Rep. C, 1980, 60(1): 1-57[5] Mclaughlin D W. J. Mathe. Phys., 1972, 13 (5): 1099-1 108[6] Mclaughlin D W. J. Math. Phys., 1972, 13 (4) 784-796[7] Callan C G, Coleman S. Phys. Rev. D, 1977, 16 (6): 1762-1768[8] Clark T E, Menikoff R, Sharp D H. Phys. Rev. D, 1980, 22 (12): 3012-3016[9] Caveau B, Schulman L S. J. Phys. A, 1986, 19 (8): 1833-1846[10] Farhi E, Gutmann S. AM. Phys., 1992, 213 (1): 182-203[11] Fwhi E, Gutmann S. IntJour. Mod. Phys. A, 1990, 5(15): 3029-3051[12] Carreau M, Farhi E, Gutmann S. Phys. Rev. D, 1990, 42 (4): 1194-1202[13] Zhang Z C, Li C S, Wei Y S. Commun. Theor. Phys., 1993, 20 (4): 461-470[14] Zhang Z C, Li C S, Wei Y S. Commun. Theor. Phys., 1994, 21 (2): 223-232[15] Karlin S, Taylor H M. A first Course in Stochastic Processes. New York: Academic Press(Second Edition),1975. 79-121[16] Wang Z X, Guo D R Introduction to Special Functions (in Chinese). Beijing: Academic Press, 1965. 440-443(王竹溪, 郭敦仁, 特殊函数概论。北京:科学出版社, 1965)
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Zhang Zhongcan, Hu Chenguo and Fang Zhenyun. Path Integral of the Angular Momentum Eigenstates Evolving Whitthe Parameter Linked With Rotation Angle Under the Space Rotation Transformation[J]. Chinese Physics C, 1998, 22(2): 153-161.
Zhang Zhongcan, Hu Chenguo and Fang Zhenyun. Path Integral of the Angular Momentum Eigenstates Evolving Whitthe Parameter Linked With Rotation Angle Under the Space Rotation Transformation[J]. Chinese Physics C, 1998, 22(2): 153-161. shu
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Received: 1900-01-01
Revised: 1900-01-01
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Path Integral of the Angular Momentum Eigenstates Evolving Whitthe Parameter Linked With Rotation Angle Under the Space Rotation Transformation

    Corresponding author: Zhang Zhongcan,
  • Department of Physics ,Chongqing University, Chongqing 630044

Abstract: We study the method which directly adopts the azimuthal angles and the rotation angle of the axis to describe the evolving process of the angular momentum eigenstates under the space rotation transformation we obtain the angular momentum rotation and multi-rotation matrix elements ' path integral which evolves with the parameter λ(0→θ,θ the rotation angle), and establish the general method of treating the functional (path) integral as a normal multi-integrals.

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