Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

doi:10.1088/1674-1056/22/2/020304

Abstract We study the d-dimensional Schrödinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions. Numerical results are also computed for the energy spectrum and the potentials.

Keywords: parametric Nikiforov-Uvarov method new approximation scheme Eckart plus Hylleraas potential

Received: 01 June 2012
Revised: 28 June 2012
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	03.65.-w	(Quantum mechanics)
	03.65.Ca	(Formalism)

Corresponding Authors: Akpan N. Ikot, Oladunjoye A. Awoga, Akaninyene D. Antia
E-mail: ndemikot2005@yahoo.com; ola.awoga@yahoo.com; antiacauchy@yahoo.com

Cite this article:

Akpan N. Ikot, Oladunjoye A. Awoga, Akaninyene D. Antia Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential 2013 Chin. Phys. B 22 020304

[1]	Gomul O and Kocak M 2001 arxiv: Quant-Ph/0106144
[2]	Oyewumi K J, Akinpelu F O and Agboola A.D 2008 Int. J. Theor. Phys. 47 1039
[3]	Ikot A N and Akpabio L E 2010 Appl. Phys. Res. 2 202
[4]	Ikot A N, Akpabio L E and Umoren E B 2011 J. Sci. Res. 3 25
[5]	Hassanabadi H, Zurrinkamar S and Rahimov H 2011 Commun. Theor. Phys. 56 423
[6]	Greene R L and Aldrich C 1976 Phys. Rev. A 14 2363
[7]	Ikot A N 2011 Afr. Phys. Rev. 6 221
[8]	Zhang A P, Qiang W C and Ling Y W 2006 Chin. Phys. Lett. 26 100302
[9]	Wei G F, Long C Y, Duan X Y and Dong S H 2008 Phys. Scr. 77 035001
[10]	Qiang W C and Dong S H 2009 Phys. Scr. 79 045004
[11]	Bayrak O, Kocak G and Boztosun I 2006 J. Phys A: Math. Gen. 39 11521
[12]	Dong S H and Garcia-Ravelo J 2007 Phys. Scr. 75 307
[13]	Jia C S, Guo P and Peng X L 2006 J. Phys. A: Math. Gen. 39 7737
[14]	Taskin F and Kocak G 2010 Chin. Phys. B 19 090314
[15]	Ikot A N, Akpabio L E and Obu J A 2011 J. Vect. Relat. 6 1
[16]	Ikot A N, Awoga O A, Akpabio L E and Antia A D 2011 Elixir. Vib. Spec. 33 2303
[17]	Ikot A N, Antia A D, Akpabio L E and Obu J A 2011 J. Vect. Relat. 6 65
[18]	Yasuk F, Durwins A and Boztsun I 2006 J. Math. Phys. 47 083202
[19]	Falaye B J and Oyewumi K J 2011 Afri. Phys. Rev. 6 0025
[20]	Ikhadair S M and Sever R 2007 J. Math. Chem. 42 461
[21]	Ikhadair S M and Sever R 2007 Int. J. Theor. Phys. 46 1643
[22]	Ikhadair S M 2008 Chin. J. Phys. 46 291
[23]	Ikhadair S M and Sever R 2008 Cent. Eur. J. Phys. 6 685
[24]	Varshni Y P 1957 Rev. Mod. Phys. 29 664
[25]	Hylleraas E A 1935 J. Chem. Phys. 3 595
[26]	Cardose J L and Alvarez-Nodarse R 2003 J. Phys. A: Math. Gen. 36 2055
[27]	Dong S H and Sun G H 2003 Phys. Lett. A 314 261
[28]	Dong S H, Chen C Y and Cassou M L 2005 J. Phys. B 38 2211
[29]	Oyewumi K J and Ogunsola A W 2004 J. Pure Appl. Sci. 10 343
[30]	Paz G 2011 Eur. J. Phys. 22 337
[31]	Dong S H, Sun G H and Popov D 2003 J. Math. Phys. 44 4467
[32]	Ikhadair S M and Sever R 2008 Mol. Struc: THEOCHEM 855 13
[33]	Dong S H and Ma Z Q 2002 Phys. Rev. A 65 042717
[34]	Nikiforov A F and Uvarov V B 1998 Special Functions of Mathematical Physics (Basel: Birkhauser)
[35]	Tezcan C and Sever R 2009 Int. J. Theor. Phys. 48 337
[36]	Arda A, Sever R and Tezcan C 2010 Chin. J. Phys. 48 27
[37]	Hassanabadi H, Zarrinkamar S and Rajabi A A 2011 Commun. Theor. Phys. 55 541
[38]	Dong S H, Qiang W C, Sun G H and Bezerra V B 2007 J. Phys. A: Math. Theor. 40 10535
[39]	Ikhadair S M 2009 Eur. Phys. J. A 39 307
[40]	Debnath S and Biswas B 2012 EJTP 26 191
[41]	Abramowitz M and Stegun I A 1972 Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (New York: Dover)
[42]	Polyanin A D and Manzhirov A V 1998 Handbook of Integral Equations (Boca Raton: CRC Press)
[43]	Gradshteyn I S and Rhyzhik I M 2007 Table of Integrals, Series and Product (Burlington: Elsevier)

[1]	Propagation and modulational instability of Rossby waves in stratified fluids Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Chin. Phys. B, 2022, 31(7): 070202.
[2]	Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system Yi-Cai Zhang(张义财). Chin. Phys. B, 2022, 31(5): 050311.
[3]	Exact solutions of the Schrödinger equation for a class of hyperbolic potential well 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). Chin. Phys. B, 2022, 31(4): 040301.
[4]	Geometric quantities of lower doubly excited bound states of helium Chengdong Zhou(周成栋), Yuewu Yu(余岳武), Sanjiang Yang(杨三江), and Haoxue Qiao(乔豪学). Chin. Phys. B, 2022, 31(3): 030301.
[5]	Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Chin. Phys. B, 2021, 30(11): 110202.
[6]	Thermodynamic properties of massless Dirac-Weyl fermions under the generalized uncertainty principle Guang-Hua Xiong(熊光华), Chao-Yun Long(龙超云), and He Su(苏贺). Chin. Phys. B, 2021, 30(7): 070302.
[7]	Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential Eyube E S, Rawen B O, and Ibrahim N. Chin. Phys. B, 2021, 30(7): 070301.
[8]	Wave packet dynamics of nonlinear Gazeau-Klauder coherent states of a position-dependent mass system in a Coulomb-like potential Faustin Blaise Migueu, Mercel Vubangsi, Martin Tchoffo, and Lukong Cornelius Fai. Chin. Phys. B, 2021, 30(6): 060309.
[9]	A local refinement purely meshless scheme for time fractional nonlinear Schrödinger equation in irregular geometry region Tao Jiang(蒋涛), Rong-Rong Jiang(蒋戎戎), Jin-Jing Huang(黄金晶), Jiu Ding(丁玖), and Jin-Lian Ren(任金莲). Chin. Phys. B, 2021, 30(2): 020202.
[10]	A meshless algorithm with the improved moving least square approximation for nonlinear improved Boussinesq equation Yu Tan(谭渝) and Xiao-Lin Li(李小林). Chin. Phys. B, 2021, 30(1): 010201.
[11]	Transparently manipulating spin-orbit qubit via exact degenerate ground states Kuo Hai(海阔), Wenhua Zhu(朱文华), Qiong Chen(陈琼), Wenhua Hai(海文华). Chin. Phys. B, 2020, 29(8): 083203.
[12]	Simulation of anyons by cold atoms with induced electric dipole moment Jian Jing(荆坚), Yao-Yao Ma(马瑶瑶), Qiu-Yue Zhang(张秋月), Qing Wang(王青), Shi-Hai Dong(董世海). Chin. Phys. B, 2020, 29(8): 080303.
[13]	Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field Yi Yang(杨毅), Shao-Hong Cai(蔡绍洪), Zheng-Wen Long(隆正文), Hao Chen(陈浩), Chao-Yun Long(龙超云). Chin. Phys. B, 2020, 29(7): 070302.
[14]	Unified approach to various quantum Rabi models witharbitrary parameters Xiao-Fei Dong(董晓菲), You-Fei Xie(谢幼飞), Qing-Hu Chen(陈庆虎). Chin. Phys. B, 2020, 29(2): 020302.
[15]	Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards Runzu Zhang(张润祖), Weihua Zhang(张为华), Barbara Dietz, Guozhi Chai(柴国志), Liang Huang(黄亮). Chin. Phys. B, 2019, 28(10): 100502.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

Cite this article:

Online attention