The nonrelativistic oscillator strength of a hyperbolic-type potential

doi:10.1088/1674-1056/22/6/060202

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60202-060202.doi: 10.1088/1674-1056/22/6/060202

The nonrelativistic oscillator strength of a hyperbolic-type potential

H. Hassanabadi^a, S. Zarrinkamar^b, B. H. Yazarloo^a

a Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran;
b Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

收稿日期:2012-09-09 修回日期:2012-11-14 出版日期:2013-05-01 发布日期:2013-05-01

The nonrelativistic oscillator strength of a hyperbolic-type potential

H. Hassanabadi^a, S. Zarrinkamar^b, B. H. Yazarloo^a

a Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran;
b Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

Received:2012-09-09 Revised:2012-11-14 Online:2013-05-01 Published:2013-05-01
Contact: B. H. Yazarloo E-mail:hoda.yazarloo@gmail.com

摘要/Abstract

摘要： We consider the D-dimensional Schrödinger equation under the hyperbolic potential V₀ (1-coth (αr)) +V₁ (1-coth (αr))². Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.

关键词: Schrö, dinger equation, D-dimensional space, hyperbolic potential, supersymmetry quantum mechanics, oscillator strength

Abstract: We consider the D-dimensional Schrödinger equation under the hyperbolic potential V₀ (1-coth (αr)) +V₁ (1-coth (αr))². Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.

Key words: Schrödinger equation, D-dimensional space, hyperbolic potential, supersymmetry quantum mechanics, oscillator strength

中图分类号: (Special functions)

02.30.Gp

03.65.-w (Quantum mechanics) 03.65.Ge (Solutions of wave equations: bound states) 34.20.Cf (Interatomic potentials and forces)

H. Hassanabadi, S. Zarrinkamar, B. H. Yazarloo. The nonrelativistic oscillator strength of a hyperbolic-type potential[J]. 中国物理B, 2013, 22(6): 60202-060202.

H. Hassanabadi, S. Zarrinkamar, B. H. Yazarloo. The nonrelativistic oscillator strength of a hyperbolic-type potential[J]. Chin. Phys. B, 2013, 22(6): 60202-060202.

参考文献 38

[1]	Dong S H 2002 Phys. Scr. 65 289
[2]	Qiang W C and Dong S H 2005 Phys. Scr. 72 127
[3]	Dong S H and Ma Z Q 2002 Phys. Rev. A 65 042717
[4]	Qiang W C and Dong S H 2008 Phys. Lett. A 372 4789
[5]	Gu X Y and Dong S H 2011 J. Math. Chem. 49 2053
[6]	Hassanabadi H, Yazarloo B H, Zarrinkamar S and Rahimov H 2012 Commun. Theor. Phys. 57 339
[7]	Dong S H, Lozada-Cassou M, Yu J, Jimenez-Angeles F and Rivera A L 2007 Int. J. Quantum Chem. 107 366
[8]	Dong S H, Chen C Y and Cassou M L 2005 J. Phys. B 38 2211
[9]	Dong S H, Sun G H and Cassou M L 2005 Int. J. Quantum Chem. 102 147
[10]	Chen G 2004 Phys. Scr. 69 257
[11]	Wei G F, Sun G H and Dong S H 2012 Appl. Math. Comput. 218 11171
[12]	Dong S H and Cassou M L 2004 Int. J. Mod. Phys. E 13 917
[13]	Wei G F and Dong S H 2011 Can. J. Phys. 89 1225
[14]	Dong S H and Gonzalez-Cisneros A 2008 Ann. Phys. 323 1136
[15]	Ma Z Q, Dong S H, Gu X Y and Lozada-Cassou M 2004 Int. J. Mod. Phys. E 13 597
[16]	Dong S H, Sun G H and Popov D 2003 J. Math. Phys. 44 4467
[17]	Gu X Y, Ma Z Q and Dong S H 2003 Phys. Rev. A 67 062715
[18]	Yu J, Dong S H and Sun G H 2004 Phys. Lett. A 322 290
[19]	Hassanabadi S, Rajabi A A, Yazarloo B H, Zarrinkamar S and Hassanabadi H 2012 Advances in High Energy Physics, Volume 2012, Article ID 804652
[20]	Hassanabadi H, Rahimov H and Zarrinkamar S 2012 Advances in High Energy Physics Volume 2011, Article ID 458087
[21]	Walz M, Neu R, Staudt G, Oberhummer H and Cech H 1988 J. Phys. G: Nucl. Part. Phys. 14 L91
[22]	Garcia F, Garrote E, Yoneama M L, Arruda-Neto J D T, Mesa J, Bringas F, Bringas J F, Likhachev V P, Rodriguez O and Guzman F 1999 Eur. Phys. J. A 6 49
[23]	Bespalova O V, Romanovsky E A and Spasskaya T I 2003 J. Phys. G: Nucl. Part. Phys. 29 1193
[24]	Dasgupta M, Hinde D J, Newton J O and Haginon K 2004 Prog. Theor. Phys. Suppl. 154 209
[25]	Ogloblin A A, Glukhov Yu A, Trzaska W H, Dem'yanova A S, Goncharov S A, Julin R, Klebnikov S V, Mutterer M, Rozhkov M V, Rudakov V P, Tiorin G P, Khoa Dao T and Satchler G R 2000 Phys. Rev. C 62 044601
[26]	Clemenger K 1985 Phys. Rev. B 32 1359
[27]	Junker G 1996 Supersymmetric Methods in Quantum and Statistical Physics (Berlin: Springer-Verlag)
[28]	Dong S H 2007 Factorization Method in Quantum Mechanics (Netherlands: Springer)
[29]	Agboola D 2010 Chin. Phys. Lett. 27 040301
[30]	Dong S H 2011 Wave Equations in Higher Dimensions (Berlin: Springer)
[31]	Jia C S, Liu J Y and Wang P Q 2008 Phys. Lett. A 372 4779
[32]	Hellmann G 1937 Einfhrung in die Quantenchemie (Leipzig: Deutiche)
[33]	Feynman R P 1939 Phys. Rev. 56 340
[34]	Agboola D 2009 Phys. Scr. 80 065304
[35]	Hibbert A 1975 Rep. Prog. Phys. 38 1217
[36]	Lu L L, Xie W F and Hassanabadi H 2011 J. Lumin. 131 2538
[37]	Hassanabadi H, Yazarloo B H and Lu L L 2012 Chin. Phys. Lett. 29 020303
[38]	Light J C, Hamiltonian I P and Lill J V 1985 J. Chem. Phys. 82 1400

The nonrelativistic oscillator strength of a hyperbolic-type potential

The nonrelativistic oscillator strength of a hyperbolic-type potential

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