Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

doi:10.1088/1674-1056/20/1/010304

中国物理B ›› 2011, Vol. 20 ›› Issue (1): 10304-010304.doi: 10.1088/1674-1056/20/1/010304

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

唐文林, 田贵花

School of Science, Beijing University of Posts And Telecommunications, Beijing 100876, China

修回日期:2010-09-15 出版日期:2011-01-15 发布日期:2011-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002).

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Tang Wen-Lin(唐文林)^† and Tian Gui-Hua(田贵花)^‡

School of Science, Beijing University of Posts And Telecommunications, Beijing 100876, China

Revised:2010-09-15 Online:2011-01-15 Published:2011-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002).

摘要/Abstract

摘要： The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Abstract: The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Key words: spheroidal wave equation, the perturbation method in supersymmetric quantum mechanics, super-potential, eigenvalue and eigenfunction

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

02.30.Gp (Special functions) 11.30.Pb (Supersymmetry)

唐文林, 田贵花. Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method[J]. 中国物理B, 2011, 20(1): 10304-010304.

Tang Wen-Lin(唐文林) and Tian Gui-Hua(田贵花). Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method[J]. Chin. Phys. B, 2011, 20(1): 10304-010304.

参考文献 17

[1]	Grunbaum F and Miranian L 2001 Proc.SPIE bf4478 151
[2]	Teukolsky S A 1973 J.Astrophys. bf185 635
[3]	Madan Lal Mehta 2006 Random Matrices (Beijing: Beijing World Publishing Corporation) Chap.6
[4]	Emanuele Berti, Vitor Cardoso and Marc Casals 2006 arXiv:gr-qc/0511111v4
[5]	Flammer C 1956 Spheroidal Wave Functions (Stanford, CA: Stanford University) Chap.1,2,3
[6]	Press W and Teukolsky S 1973 J. Astrophys. 185 649
[7]	Fackerell E D and Crossman R G 1977 J. Math. Phys. bf18 1849
[8]	Seidel E 1989 Class. Quant. Grav. bf6 1057
[9]	Tian G H and Zhong S Q 2009 arXiv:gr-qc/0906.4685v2
[10]	Tian G H and Zhong S Q 2010 Chin. Phys. Lett. 27 040305
[11]	Zhao Y H, Hai W H, Zhao C L and Luo X B 2008 Chin. Phys. B 17 1720
[12]	Xu T 2010 Chin. Phys. B 19 080690
[13]	Tian G H and Zhong S Q 2009 arXiv:gr-qc/0906.4687v2
[14]	Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 268
[15]	Infeld L and Hull T E 1951 Rev. Mod. Phys. 23 21
[16]	Wang Z X and Guo D R 2000 Special Function (Beijing: Peking University Press) Chap.2,3,4
[17]	Andrews G E, Askey R A and Roy R 1993 Special Function (Cambridge: Cambridge University Press) Chap.1,2,3 endfootnotesize

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

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