Exact Solutions of Non-spherical Harmonic Oscillator Potential

Chen Changyuan; Liu Youwen

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

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

Abstract
HTML
Reference
Related

PDF

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)

[1]	XU Qiang , ZHU Sheng-Jiang . Splitting of Pseudospin and Spin Partners in the Relativistic Harmonic Oscillator. Chinese Physics C, 2007, 31(3): 251-257.
[2]	WANG Jian-Hua , LI Kang , LIU Peng . Energy Splitting of Isotropic Harmonic Oscillator in Noncommutative Phase Space. Chinese Physics C, 2006, 30(5): 387-391.
[3]	CHENG Yan-Fu , DAI Tong-Qing . Multiple-scale Perturbation Theory of Sextic Anharmonic Oscillator. Chinese Physics C, 2006, 30(6): 513-516.
[4]	CHENG Yan-Fu , DAI Tong-Qing . Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator. Chinese Physics C, 2006, 30(10): 944-949.
[5]	An Nan , YANG Xin-E . Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition. Chinese Physics C, 2005, 29(4): 350-353.
[6]	WANG Peng , WANG Shun-Jin . Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator. Chinese Physics C, 2005, 29(7): 651-656.
[7]	WANG Zhong-Qing , ZHOU Ping , ZHU Lian-Xuan , DAI Hong-Ying . Superposition of Generalized q-Coherent States of the Non-harmonicOscillator and Their Nonclassical Properties. Chinese Physics C, 2004, 28(4): 365-369.
[8]	WANG Zhong-Qing . Antibunching Properties for the Eigenstates of the Higher Powers of Annihilation Operator of a q-Deformed Non-harmonic Oscillator. Chinese Physics C, 2003, 27(2): 105-108.
[9]	WANG Ji-Suo , FENG Jian , LIU Tang-Kun , ZHAN Ming-Sheng . Antibunching Effect of Eigenstates of the Operator bQ－K in a Q-Deformed Non-harmonic Oscillator. Chinese Physics C, 2002, 26(6): 569-575.
[10]	WANG Zhong-Qing . Higher Power Squeezing Properties for Odd and Even Two-Parameter Deformed Coherent States. Chinese Physics C, 2001, 25(12): 1158-1164.
[11]	WANG Zhong-Qing . Higher-Order Squeezing and Antibunching Effect for the Odd and Even Generalized q-Coherent States of the Non-harmonic Oscillator. Chinese Physics C, 2001, 25(11): 1044-1050.
[12]	WANG Ji-Suo , LIU Tang-Kun , ZHAN Ming-Sheng . Higher-Order Squeezing for Generalized Odd and Even Coherent States of a Q-Deformed Non-harmonic Oscillator. Chinese Physics C, 2001, 25(1): 11-15.
[13]	WANG JiSuo , LIU TangKun , ZHAN MingSheng . Eigenstates of the Higher Powers of Annihilation Operator of a Q-Deformed Non-harmonic Oscillator and Their Higher-Order Squeezing. Chinese Physics C, 2000, 24(12): 1115-1122.
[14]	Xu Ziwen . Q-Deformation of Generalized Coherent States in the Non-harmonic Oscillator Potential. Chinese Physics C, 1999, 23(5): 436-444.
[15]	Ma Tao , Ni Zhixiang . Non-Harmonic Oscillator and New Conditionally Exactly Solvable Potentials. Chinese Physics C, 1999, 23(7): 650-654.
[16]	Wang Jisuo , Sun Changyong , He Jinyu . Eigenstates of the Higher Power of the Annihilation Operator ofTwo-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1996, 20(8): 703-706.
[17]	Zhou Huanqiang , He Jingsong , Zhang Xinming . Eigenstates of the Second Power of the Annihilation Operator of Two-Parameter Deformed Harmonic Oscillator. Chinese Physics C, 1995, 19(3): 251-257.
[18]	YANG Xian-Jun , FAN Xi-Pei . State Densities of Deformed Nuclei Based on Axisymmetric Harmonic Oscillator Potential. Chinese Physics C, 1992, 16(5): 431-438.
[19]	ZHOU Yuan-Hai , JIANG De-Sun , QIAN Wen-Jia , GONG Xue-Hui . THE HEAVY QUARKONIUM SPECTRUM OF ANHARMONIC OSCILLATORS CONFINEMENT POTENTIAL. Chinese Physics C, 1987, 11(2): 202-207.
[20]	CHU CHUNG-YUAN AN ING , . A MODEL OF THE STRUCTURE OF MESONS WITH A COVARIANT OSCILLATOR POTENTIAL. Chinese Physics C, 1977, 1(1): 47-51.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1998-06-16
Revised: 1900-01-01

Article Metric

Article Views(3059)
PDF Downloads(559)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.