修正Pöschl-Teller势Schrödinger方程束缚态的近似解析解
Approximate Analytical Solutions of Bound States for Schrödinger Equation with Modified Pöschl-Teller Potential
摘要: 利用我们最近提出的关于离心项的一个新的近似表达式，获得了修正Pöschl-Teller势非S波束缚态的近似解析解，给出了能谱方程和相应的归一化的径向波函数。数值计算结果表明，由新的离心项的近似表达式获得的能量本征值和Mathematica程序包给出的计算结果很好的一致。
Abstract: We use a new approximation scheme for the centrifugal term, and present approximate analytical solutions of bound states for modified Pöschl-Teller potential with the arbitrary angular momentum states. The normalized wave functions and energy equation for bound states are given. The numerical results show that our results are in good agreement with those obtained by using the Mathematica package, and that the new approximation scheme is better than the old approximation scheme.
文章引用：陈昌远, 尤源, 陆法林. 修正Pöschl-Teller势Schrödinger方程束缚态的近似解析解[J]. 应用物理, 2012, 2(3): 82-88. http://dx.doi.org/10.12677/APP.2012.23014

参考文献

[1] S. Flügge. Practical quantum mechanics [M]. 北京: 科学出版社, 2009: 问题39, 问题93.
[2] F. Iachello, S. Oss. Algebraic model of bending vibrations of complex molecules. Chemical Physics Letters, 1993, 205(2-3): 285-289.
[3] F. Iachello, S. Oss. Vibrational spectroscopy and intramolecular relaxation of benzene. Journal of Chemical Physics, 1993, 99(10): 7337-7349
[4] M. M. Nieto. Exact wave-function normaliza-tion constants for B0tanhz-U0cosh-2z and Pöschl-Teller poten-tials. Physical Re- view A, 1978, 17(4): 1273-1283.
[5] 陈昌远, 胡嗣柱. 修正Pöschl-Teller势的Schrödinger方程束缚态的精确解[J]. 物理学报, 1995, 44(1): 9-15.
[6] 陈昌远, 孙东升, 孙国耀. 修正Pöschl-Teller势的Schrödinger方程散射态的精确解[J]. 中山大学学报(自然科学版), 1998, 37(6): 49-54.
[7] S. H. Dong, R. Lemus. Ladder operators for the modified Pöschl- Teller potential. International Journal of Quan-tum Chemistry, 2002, 86(3): 265-272.
[8] J. Zùñiga, M. Alacid, A. Requena, et al. Matrix elements for the modified Pöschl-Teller potential. International Journal of Quan- tum Chemistry, 1996, 57(1): 43-51.
[9] J. Gomez-Camacho, R. Lemus and J. M. Arias. Matrix elements of u and p for the modi-fied Pöschl-Teller potential. Journal of Physics A, 2004, 37(19): 5237-5242.
[10] M. Rey, F. Michelot. Matrix elements for powers of x-dependent operators for the hyperbolic Pöschl-Teller potentials. Journal of Physics A, 2009, 42: Article ID: 165209.
[11] O. Bayrak, G. Kocak and I. Boztosun. Any l-state solutions of the Hulthén potential by the asymptotic itera-tion method. Jour- nal of Physics A, 2006, 39: 11521-11529.
[12] 陈昌远, 陆法林, 孙东升. Hulthén势散射态的解析解[J]. 物理学报, 2007, 56(11): 6204-6208.
[13] S. H. Dong, W. C. Qiang, G. H. Sun, et al. Analytical approxi- mations to the l-wave solutions of the Schrödinger equation with the Eckart potential. Journal of Physics A, 2007, 40: 10535- 10540.
[14] C. Y. Chen, D. S. Sun and F. L. Lu. Analytical ap-proximations of scattering states to the l-wave solutions for the Schrödinger equation with the Eckart potential. Journal of Phys-ics A, 2008, 41: Article ID: 035302.
[15] G. F. Wei, C. Y. Long, X. Y. Duan, et al. Arbitrary l-wave scat- tering state solutions of the Schrödinger equation for the Eckart potential. Physica Scripta, 2008, 77(3): Article ID: 035001.
[16] W. C. Qiang, S. H. Dong. Analytical approximations to the solu- tions of the Manning-Rosen potential with centrifugal term. Physical Letters A, 2007, 368(1-2): 13-17.
[17] G. F. Wei, C. Y. Long and S. H. Dong. The scattering of the Manning-Rosen potential with cen-trifugal term. Physics Letters A, 2008, 372(15): 2592-2596.
[18] D. Agboola. Solutions to the modified Pöschl-Teller potential in D-Dimensions. Chinese Physics Let-ters, 2010, 27(4): Article ID: 040301.
[19] C. Y. Chen, F. L. Lu and Y. You. Scattering states of modified Pöschl-Teller potential in D-dimension. Chinese Physics B, 2012, 21(3): Article ID: 030302.
[20] W. Lucha, F. F. Schöberl. Solving the Schrödinger equation for bound states with MATHEMATICA 3.0. Interna-tional Journal of Modern Physics C, 1999, 10(4): 607-619.
[21] 王竹溪, 郭敦仁. 特殊函数概论[M]. 北京: 北京大学出版社, 2000: 第4章.
[22] 刘式适, 刘式达. 特殊函数(第2版)[M]. 北京: 气象出版社, 2002: 第8章.
[23] I. S. Gradshteyn, I. M. Ryzhik. 2000 tables of integrals, series, and products (6th edition) [M]. 北京: 世界图书出版公司北京公司, 2000: 第8章, 第9章.
[24] G. F. Wei, S. H. Dong. A novel algebraic approach to spin sym- metry for Dirac equation with scalar and vector sec-ond Pöschl- Teller potentials. The European Physical Journal A, 2010, 43(2): 185-190.
[25] Y. Xu, S. He and C. S. Jia. Ap-proximate analytical solutions of the Dirac equation with the Pöschl-Teller potential including the spin-orbit coupling term. Journal of Physics A, 2008, 41: Article ID: 255302.
[26] J. Lu, H. X. Qian, L. M. Li, et al. Rotation and vibration of dia-tomic molecule oscillator with hyperbolic potential function. Chinese Physics B, 2005, 14(12): 2042-2046.

为你推荐