Exact Solutions of Non-spherical Harmonic Oscillator Potential

  • In this paper, the Schrodinger equation with a non-spherical harmonic oscillator potential in three dimensions V(r)=1/2r2+A/2r2 is solved. The exact energy equation and the normalized wave function are obtained. The calculation formulas andrecurrence formulas of matrix elements and mean values for any integer power operator rs are presented.
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  • [1] Zhu Dongpei.J.Phys.A.,1987,20(13):4331—43362 Chen Changyuan, Liu Youwen.Acta Physica Sinica(in Chinese),1998,47(4):536—541 (陈昌远,刘友文.物理学报,1998,47(4):536—541) 3 Xu Ziwen.Acta Physica Sinica(in Chinese), 1996, 45(11):1807—1811 (徐子.物理学报,1996,45(11):1807—1811)4 Ni Zhixiang. Acta Physica Sinica(in Chinese),1997,46(9):1687—1692 (倪致样.物理学报,1997,46(9):1687—1692) 5 Yu Zhaoxian, Wang Jisuo, Liu Yehou. Acta Physica Sinica (in Chinese),1997,46(9):1693—1698 (于肇贤,王继锁,刘业厚.物理学报,1997,46(9):1693—1698)6 Landau L D, Lifshitz E M. Quantum Mechanics. 3rd ed. New York: Pergamon Press, 1977. 114—117 7 Wand Zhuxi, Guo Dunren. An Introduction to Special Functions (in Chinese).Beijing:Science Press,1979. 361—365 (王竹溪,郭敦仁.特殊函数概论.北京:科学出版社,1979.361—365)8 Zeng Jinyan. Quantum Mechanics (in Chinese). Vol 1.2nd ed.Beijing:Science Press,1997.283—286 (曾谨言.量子力学卷I.第二版.北京:科学出版社,1997.283—286) 9 Goldhammer P. Rev. Mod. Phys., 1963, 35(1):40—107 10 Qian Bochu, Zeng JInyan. Problems Choice and Dissection in Quantum Mechanics (in Chinese). Beijing: Science Press, 1988. 202—204(钱伯初,曾谨言.量子力学习题精选与剖析.北京:科学出版社,1988.202—204)
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Chen Changyuan and Liu Youwen. Exact Solutions of Non-spherical Harmonic Oscillator Potential[J]. Chinese Physics C, 1999, 23(9): 865-872.
Chen Changyuan and Liu Youwen. Exact Solutions of Non-spherical Harmonic Oscillator Potential[J]. Chinese Physics C, 1999, 23(9): 865-872. shu
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Received: 1998-06-16
Revised: 1900-01-01
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Exact Solutions of Non-spherical Harmonic Oscillator Potential

    Corresponding author: Chen Changyuan,
  • Department of Physics, Yancheng Teachers' College, Yancheng 224002

Abstract: In this paper, the Schrodinger equation with a non-spherical harmonic oscillator potential in three dimensions V(r)=1/2r2+A/2r2 is solved. The exact energy equation and the normalized wave function are obtained. The calculation formulas andrecurrence formulas of matrix elements and mean values for any integer power operator rs are presented.

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