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

Zhang Zhongcan; Hu Chenguo; Fang Zhenyun

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1998, Vol. 22> Issue(2) : 153-161

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

Department of Physics ,Chongqing University, Chongqing 630044

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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.

References

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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.

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1998-02-05

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.