Scattering states of modified Pöschlben–Teller potential in D-dimension

doi:10.1088/1674-1056/21/3/030302

中国物理B ›› 2012, Vol. 21 ›› Issue (3): 30302-030302.doi: 10.1088/1674-1056/21/3/030302

Scattering states of modified Pöschlben–Teller potential in D-dimension

陈昌远,陆法林,尤源

收稿日期:2011-05-29 修回日期:2011-10-22 出版日期:2012-02-15 发布日期:2012-02-15
通讯作者: 陈昌远,yctcccy@163.net E-mail:yctcccy@163.net

Scattering states of modified Pöschlben–Teller potential in D-dimension

Chen Chang-Yuan(陈昌远)^†, Lu Fa-Lin(陆法林), and You Yuan(尤源)

School of Physics and Electronics, Yancheng Teachers University, Yancheng 224002, China

Received:2011-05-29 Revised:2011-10-22 Online:2012-02-15 Published:2012-02-15
Contact: Chen Chang-Yuan,yctcccy@163.net E-mail:yctcccy@163.net
Supported by:
Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010291).

摘要/Abstract

Abstract: We present a new approximation scheme for the centrifugal term, and apply this new approach to the Schr?dinger equation with the modified P?schl-Teller potential in the D-dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the $k/2\pi$ scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method (APM).

Key words: modified P?schl-Teller potential in D-dimension, Schr?dinger equation, scattering states

中图分类号: (Scattering theory)

03.65.Nk

03.65.Db (Functional analytical methods)

陈昌远, 陆法林, 尤源. Scattering states of modified Pöschlben–Teller potential in D-dimension[J]. 中国物理B, 2012, 21(3): 30302-030302.

Chen Chang-Yuan(陈昌远), Lu Fa-Lin(陆法林), and You Yuan(尤源) . Scattering states of modified Pöschlben–Teller potential in D-dimension[J]. Chin. Phys. B, 2012, 21(3): 30302-030302.

参考文献 39

[1]	Fl黦ge S 1999 Practical Quantum Mechanics (Berlin: Springer Press)
[2]	Carrington T 1990 J. Mol. Phys. 70 757
[3]	Iachello F and Oss S 1993 Chem. Phys. Lett. 205 285
[4]	Iachello F and Oss S 1993 J. Chem. Phys. 99 7337
[5]	Nieto M M 1978 Phys. Rev. A 17 1273
[6]	Chen C Y and Hu S Z 1995 Acta Phys. Sin. 44 9 (in Chinese)
[7]	Dong S H and Lemus R 2002 Int. J. Quantum Chem. 86 265
[8]	Z`u niga J, Alacid M, Requena A and Bastida A 1996 Int. J. Quantum Chem. 57 43
[9]	Gomez-Camacho J, Lemus R and Arias J M 2004 J. Phys. A: Math. Gen. 37 5237
[10]	Rey M and Michelot F 2009 J. Phys. A: Math. Theor. 42 165209
[11]	Dong S H 2011 Wave Equations in Higher Dimensions (Berlin: Springer Press)
[12]	Nieto M M 1979 Am. J . Phys. 47 1067
[13]	Y? nez R J, Assche W V and Dehesa J S 1994 Phys. Rev. A 50 3065
[14]	Liu Y F and Zeng J Y 1997 Science in China A 40 1110
[15]	Zeng J Y 2000 Quantum Mechanics (Vol. II, 3rd Edn.) (Beijing: Science Press) Ch. 8 (in Chinese)
[16]	Qian Y K and Zeng J Y 1993 Science in China A 36 595
[17]	Chen C Y, Sun D S, Liu C L and Lu F L 2003 Acta Phys. Sin. 52 781 (in Chinese)
[18]	Louck J D and Schaffer W H 1960 J. Mol. Spec. 4 285
[19]	Louck J D 1960 J. Mol. Spec. 4 298;
[20]	Chen C Y 2000 Chin. Phys. 9 731
[21]	Agboola D 2009 Phys. Scr. 80 065304
[22]	Chen C Y, Sun D S, Liu C L and Lu F L 2011 Commun. Theor. Phys. 55 399
[23]	Agboola D 2010 Chin. Phys. Lett. 27 040301
[24]	Jia C S, Liu J Y and Wang P Q 2008 Phys. Lett. A 372 4779
[25]	Qiang W C, Chen W L, Li K and Zhang H P 2009 Inter. J. Mod. Phys. A 24 5523
[26]	Wei G F, Chen W L, Wang H Y and Li Y Y 2009 Chin. Phys. B 18 3663
[27]	Tacskin F and Koccak G 2010 Chin. Phys. B 19 090314
[28]	Qiang W C, Li K and Chen W L 2009 J. Phys. A 42 25306
[29]	Sameer M I 2011 Phys. Scr. 83 015010
[30]	Qiang W C and Dong S H 2009 Phys. Scr. 79 045004
[31]	Landau L D and Lifshitz E M 1977 Quantum Mechanics, Non-Relativistic Theory (3rd Edn.) (Oxford: Pergamon)
[32]	Zeng J Y 2000 Quantum Mechanics (Vol. 1, 3rd Edn.) (Beijing: Science Press) Ch. 13 (in Chinese)
[33]	Chen C Y, Sun D S and Lu F L 2004 Phys. Lett. A 330 424
[34]	Wang Z X and Guo D R 1979 An Introduction to Special Functions (Beijing: Science Press) (in Chinese)
[35]	Gradshteyn I S and Ryzhik I M 2000 Tables of Integrals, Series, and Products (6th Edn.) (New York: Academic Press)
[36]	Milne W E 1930 Phys. Rev. 35 863
[37]	Wheeler J A 1937 Phys. Rev. 52 1123
[38]	Thylwe K E 2008 J. Phys. A 41 115304
[39]	Thylwe K E 2008 Phys. Scr. 77 065005

Scattering states of modified Pöschlben–Teller potential in D-dimension

Scattering states of modified Pöschlben–Teller potential in D-dimension

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