Exact Solutions of Non-spherical Harmonic Oscillator Potential

Chen Changyuan; Liu Youwen

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2024年10月30日

Chinese Physics C> 1999, Vol. 23> Issue(9) : 865-872

Exact Solutions of Non-spherical Harmonic Oscillator Potential

Chen Changyuan ^, ,
Liu Youwen

Department of Physics, Yancheng Teachers' College, Yancheng 224002

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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 r^s are presented.

References

[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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沈阳化工大学材料科学与工程学院沈阳 110142

Exact Solutions of Non-spherical Harmonic Oscillator Potential

Chen Changyuan ^,
Liu Youwen

Corresponding author: Chen Changyuan,

Department of Physics, Yancheng Teachers' College, Yancheng 224002

Received Date: 1998-06-16
Accepted Date: 1900-01-01
Available Online: 1999-09-05

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 r^s are presented.