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In the paper, we use the method of super-symmetric quantum mechanics to study the spin-weighted spheroidal wave equation in the case of s=3/2. We first change the equation into Schrdinger's form, then calculate and derive the first four terms concerning E and super-potential W. we summarize the general formula of super-potential Wn and use mathematical induction to prove its correctness. In turn, this completely gives all the information about the ground eigenvalue and eigenfunction.
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Keywords:
- spin-weighted spheroidal wave equation /
- super-symmetric quantum mechanics /
- super-potential /
- exited state wave functions
[1] Teukolsky S 1972 Phys. Rev. Lett. 29 1114
[2] Teukolsky S 1973 Astrophys. J. 185 635
[3] Emanuele Berti, Vitor Cardoso, Marc Casals 2006 Phys. Rev. D 73 024013
[4] Leaver E 1986 J. Math. Phys. 27 1238
[5] Breuer R, Ryan Jr, Waller S 1977 Proc. R. Soc. London A 358 71
[6] Press W, Teukolsky S 1973 Astrophys. J. 185 649
[7] Fackerell E, Grossman R 1977 J. Math. Phys. (N.Y.) 18 1849
[8] Ryuichi Fujita, Hideyuki Tagoshi 2004 arXiv:gr-qc/0410018 v1 5
[9] Tian G H 2010 Chin. Phys. Lett. 27 030308
[10] Tian G H, Zhong S Q 2010 Chin. Phys. Lett. 27 040305
[11] Tian G H, Zhong S Q. Arxiv: 2009, 0906.4687 V3
[12] Tian G H, Zhong S Q 2010 Sci. Chin. G 54 393
[13] Tang W L, Tian G H 2011 Chin. Phys. B 20 010304
[14] Tang W L, Tian G H 2011 Chin. Phys. B 20 050301
[15] Tian G H 2005 Chin. Phys. Lett. 22 3013
[16] Li K, Sun Y, Tian G H, Tang W L 2011 Science in China 41 729 (in Chinese)[李凯, 孙越, 田贵花, 唐文林 2011 中国科学 G 41 729]
[17] Sun Y, Tian G H, Dong K 2011 Chin. Phys. B 20 061101
[18] Dong K, Tian G H, Sun Y 2011 Chin. Phys. B 20 071101
[19] Dong K, Tian G H 2011 “Study of the Spin-weighted Spheroidal Wave Equation in the Case of s = 3/2”, Preprint
[20] Cooper F, Khare A, Sukhatme U 1995 Phys. Rep. 251 268
[21] Gradsbteyn I S, Ryzbik L M 2000 Table of integrals, series, and products. 6th ed. Singapore: Elsevierpte. Ltd
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[1] Teukolsky S 1972 Phys. Rev. Lett. 29 1114
[2] Teukolsky S 1973 Astrophys. J. 185 635
[3] Emanuele Berti, Vitor Cardoso, Marc Casals 2006 Phys. Rev. D 73 024013
[4] Leaver E 1986 J. Math. Phys. 27 1238
[5] Breuer R, Ryan Jr, Waller S 1977 Proc. R. Soc. London A 358 71
[6] Press W, Teukolsky S 1973 Astrophys. J. 185 649
[7] Fackerell E, Grossman R 1977 J. Math. Phys. (N.Y.) 18 1849
[8] Ryuichi Fujita, Hideyuki Tagoshi 2004 arXiv:gr-qc/0410018 v1 5
[9] Tian G H 2010 Chin. Phys. Lett. 27 030308
[10] Tian G H, Zhong S Q 2010 Chin. Phys. Lett. 27 040305
[11] Tian G H, Zhong S Q. Arxiv: 2009, 0906.4687 V3
[12] Tian G H, Zhong S Q 2010 Sci. Chin. G 54 393
[13] Tang W L, Tian G H 2011 Chin. Phys. B 20 010304
[14] Tang W L, Tian G H 2011 Chin. Phys. B 20 050301
[15] Tian G H 2005 Chin. Phys. Lett. 22 3013
[16] Li K, Sun Y, Tian G H, Tang W L 2011 Science in China 41 729 (in Chinese)[李凯, 孙越, 田贵花, 唐文林 2011 中国科学 G 41 729]
[17] Sun Y, Tian G H, Dong K 2011 Chin. Phys. B 20 061101
[18] Dong K, Tian G H, Sun Y 2011 Chin. Phys. B 20 071101
[19] Dong K, Tian G H 2011 “Study of the Spin-weighted Spheroidal Wave Equation in the Case of s = 3/2”, Preprint
[20] Cooper F, Khare A, Sukhatme U 1995 Phys. Rep. 251 268
[21] Gradsbteyn I S, Ryzbik L M 2000 Table of integrals, series, and products. 6th ed. Singapore: Elsevierpte. Ltd
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