Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

doi:10.1088/1674-1056/24/6/060301

中国物理B ›› 2015, Vol. 24 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/24/6/060301

Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

H. Panahi^a, S. Zarrinkamar^b, M. Baradaran^a

a Department of Physics, University of Guilan, Rasht 41635-1914, Iran;
b Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

收稿日期:2014-09-21 修回日期:2015-01-22 出版日期:2015-06-05 发布日期:2015-06-05

Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

H. Panahi^a, S. Zarrinkamar^b, M. Baradaran^a

a Department of Physics, University of Guilan, Rasht 41635-1914, Iran;
b Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

Received:2014-09-21 Revised:2015-01-22 Online:2015-06-05 Published:2015-06-05
Contact: H. Panahi, S. Zarrinkamar, M. Baradaran E-mail:t-panahi@guilan.ac.ir;zarrinkamar.s@gmail.com;marzie.baradaran@yahoo.com
About author:03.65.-w; 03.65.Fd; 03.65.Ge

摘要/Abstract

摘要： Algebraic solutions of the D-dimensional Schrödinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl(2) algebraization.

关键词: quasi-exactly solvable, Schrö, dinger equation, Killingbeck potential, sl(2) Lie algebra, representation theory

Abstract: Algebraic solutions of the D-dimensional Schrödinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl(2) algebraization.

Key words: quasi-exactly solvable, Schrödinger equation, Killingbeck potential, sl(2) Lie algebra, representation theory

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Fd (Algebraic methods) 03.65.Ge (Solutions of wave equations: bound states)

H. Panahi, S. Zarrinkamar, M. Baradaran. Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach[J]. 中国物理B, 2015, 24(6): 60301-060301.

H. Panahi, S. Zarrinkamar, M. Baradaran. Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach[J]. Chin. Phys. B, 2015, 24(6): 60301-060301.

参考文献 43

[1]	Turbiner A V 1988 Commun. Math. Phys. 118 467
[2]	Turbiner A V 1994 Contemp. Math. 160 263
[3]	Gomez-Ullate D, Kamran N and Milson R 2007 Phys. Atom. Nucl. 70 520
[4]	Gómez-Ullate D, Kamran N and Milson R 2005 J. Phys. A: Math. Gen. 38 2005
[5]	Ushveridze A G 1990 Mod. Phys. Lett. A 5 1891
[6]	Ushveridze A G 1994 Quasi-exactly Solvable Models in Quantum Mechanics (Bristol: IOP)
[7]	Zhang Y Z 2013 J. Math. Phys. 54 102104
[8]	Lee Y H, Links J and Zhang Y Z 2011 J. Phys. A: Math. Theor. 44 482001
[9]	Sasaki R 2007 J. Math. Phys. 48 122104
[10]	Sasaki R, Yang W L and Zhang Y Z 2009 SIGMA 5 104
[11]	Ho C L 2006 Ann. Phys. 321 2170
[12]	Panahi H and Baradaran M 2012 Mod. Phys. Lett. A 27 1250176
[13]	Panahi H and Baradaran M 2013 Eur. Phys. J. Plus 128 39
[14]	Fernández F M 1992 Phys. Lett. A 166 173
[15]	Roychoudhury R K, Varshni Y P and Sengupta M 1990 Phys. Rev. A 42 184
[16]	Roychoudhury R K and Varshni Y P 1988 J. Phys. A: Math. Gen. 21 3025
[17]	Chaudhuri R N 1988 J. Phys. A: Math. Gen. 21 567
[18]	Chaudhuri R N and Mondal M 1995 Phys. Rev. A 52 1850
[19]	Killingbeck J 1978 Phys. Lett. A 67 13
[20]	Plante G and Antippa A F 2005 J. Math. Phys. 46 062108
[21]	Saxena R P and Varma V S 1982 J. Phys. A: Math. Gen. 15 L221
[22]	Bessis D E, Vrscay R and Handy C R 1987 J. Phys. A: Math. Gen. 20 149
[23]	Saxena R P and Varma V S 1982 J. Phys. A: Math. Gen. 15 L149
[24]	Dong S H 2000 Int. J. Theor. Phys. 39 1119
[25]	Özer O and Gönül B 2003 Mod. Phys. Lett. A 18 2581
[26]	Rahmani S, Hassanabadi H and Zarrinkamar S 2014 Phys. Scr. 89 065301
[27]	Hassanabadi S, Ghominejad M, Zarrinkamar S and Hassanabadi H 2013 Chin. Phys. B 22 060303
[28]	Castro L B and de Castro A S 2014 Chin. Phys. B 23 090301
[29]	Eichten E, Gottfried E, Kinoshita T, Lane K D and Yan T M 1978 Phys. Rev. D 17 3090
[30]	Vrscay E R 1985 Phys. Rev. A 31 2054
[31]	Bender C M and Wu T T 1969 Phys. Rev. 184 1231
[32]	Reid C 1970 J. Mol. Spectrosc. 36 183
[33]	Austin E J 1980 Mol. Phys. 40 893
[34]	Killingbeck J 1978 Phys. Lett. A 65 87
[35]	Skupsky S 1980 Phys. Rev. A 21 1316
[36]	Cauble R, Blaha M and Davis J 1984 Phys. Rev. A 29 3280
[37]	Adhikari R, Dutt R and Varshni Y P 1989 Phys. Lett. A 141 1
[38]	Boumedjane Y, Saidi H, Hassouni S and Zerarka A 2007 Appl. Math. Comput. 194 243
[39]	Barakat T 2006 J. Phys. A: Math. Gen. 39 823
[40]	Dong S H 2011 Wave Equations in Higher Dimensions (New York: Springer)
[41]	Hassanabadi H, Rahimov H and Zarrinkamar S 2011 Ann. Phys. 523 566
[42]	Ikot A N, Hassanabadi H, Obong H P, Chad Umoren Y E, Isonguyo C N and Yazarloo B H 2014 Chin. Phys. B 23 120303
[43]	Weyl H 1931 The Theory of Groups and Quantum Mechanics (New York: Dover)

Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

Solutions of the D-dimensional Schrödinger equation with Killingbeck potential: Lie algebraic approach

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 43

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Chang-Tong Liang(梁畅通), Jing-Jing Zhang(张晶晶), and Peng-Cheng Li(李鹏程). Phase-coherence dynamics of frequency-comb emission via high-order harmonic generation in few-cycle pulse trains[J]. 中国物理B, 2023, 32(3): 33201-033201.
[2]	Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems[J]. 中国物理B, 2023, 32(3): 30506-030506.
[3]	Lei Chen(陈磊), Pan Li(李磐), He-Shan Liu(刘河山), Jin Yu(余锦), Chang-Jun Ke(柯常军), and Zi-Ren Luo(罗子人). Coupled-generalized nonlinear Schrödinger equations solved by adaptive step-size methods in interaction picture[J]. 中国物理B, 2023, 32(2): 24213-024213.
[4]	Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.
[5]	Zhi-Xian Lei(雷志仙), Qing-Yun Xu(徐清芸), Zhi-Jie Yang(杨志杰), Yong-Lin He(何永林), and Jing Guo(郭静). Photoelectron momentum distributions of Ne and Xe dimers in counter-rotating circularly polarized laser fields[J]. 中国物理B, 2022, 31(6): 63202-063202.
[6]	Li-Jun Chang(常莉君), Yi-Fan Mo(莫一凡), Li-Ming Ling(凌黎明), and De-Lu Zeng(曾德炉). Data-driven parity-time-symmetric vector rogue wave solutions of multi-component nonlinear Schrödinger equation[J]. 中国物理B, 2022, 31(6): 60201-060201.
[7]	Xiao-Hua Wang(王晓华), Chang-Yuan Chen(陈昌远), Yuan You(尤源), Fa-Lin Lu(陆法林), Dong-Sheng Sun(孙东升), and Shi-Hai Dong(董世海). Exact solutions of the Schrödinger equation for a class of hyperbolic potential well[J]. 中国物理B, 2022, 31(4): 40301-040301.
[8]	Tian-Yi Wang(王天一), Qin Zhou(周勤), and Wen-Jun Liu(刘文军). Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers[J]. 中国物理B, 2022, 31(2): 20501-020501.
[9]	Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation[J]. 中国物理B, 2022, 31(11): 110201-110201.
[10]	Shun Wang(王顺) and Wei-Chao Jiang(姜维超). Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator[J]. 中国物理B, 2022, 31(1): 13201-013201.
[11]	Shun Wang(王顺), Shahab Ullah Khan, Xiao-Qing Tian(田晓庆), Hui-Bin Sun(孙慧斌), and Wei-Chao Jiang(姜维超). Comparative study of photoionization of atomic hydrogen by solving the one- and three-dimensional time-dependent Schrödinger equations[J]. 中国物理B, 2021, 30(8): 83301-083301.
[12]	Eyube E S, Rawen B O, and Ibrahim N. Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential[J]. 中国物理B, 2021, 30(7): 70301-070301.
[13]	Zillur Rahman, M Zulfikar Ali, and Harun-Or Roshid. Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method[J]. 中国物理B, 2021, 30(5): 50202-050202.
[14]	Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. 中国物理B, 2021, 30(11): 110202-110202.
[15]	Yagang Zhang(张亚港), Yuheng Pei(裴宇恒), Yibo Yuan(袁一博), Feng Wen(问峰), Yuzong Gu(顾玉宗), and Zhenkun Wu(吴振坤). Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity[J]. 中国物理B, 2021, 30(11): 114209-114209.