Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

doi:10.1088/1674-1056/21/4/040401

中国物理B ›› 2012, Vol. 21 ›› Issue (4): 40401-040401.doi: 10.1088/1674-1056/21/4/040401

孙越,田贵花,董锟

收稿日期:2011-09-14 修回日期:2011-10-17 出版日期:2012-02-29 发布日期:2012-02-29
通讯作者: 孙越, E-mail:sunyue1101@126.com E-mail:sunyue1101@126.com

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

Sun Yue(孙越)^†, Tian Gui-Hua(田贵花), and Dong Kun(董锟)

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

Received:2011-09-14 Revised:2011-10-17 Online:2012-02-29 Published:2012-02-29
Contact: Sun Yue, E-mail:sunyue1101@126.com E-mail:sunyue1101@126.com
Supported by:
Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)

摘要/Abstract

Abstract: By using the super-symmetric quantum mechanics (SUSYQM) method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s=2. Based on the derived W₀ to W₄ the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.

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

中图分类号: (Post-Newtonian approximation; perturbation theory; related Approximations)

04.25.Nx

11.30.Pb (Supersymmetry) 03.65.Ge (Solutions of wave equations: bound states) 02.30.Gp (Special functions)

孙越,田贵花,董锟. [J]. 中国物理B, 2012, 21(4): 40401-040401.

Sun Yue(孙越), Tian Gui-Hua(田贵花), and Dong Kun(董锟) . Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2[J]. Chin. Phys. B, 2012, 21(4): 40401-040401.

参考文献 18

[1]	Teukolsky S A 1972 Phys. Rev. Lett. 29 1114
[2]	Teukolsky S A 1973 Astrophys. J. 185 635
[3]	Teukolsky S A and Press W H 1974 Astrophysical J. 193 443
[4]	Marc Casals and Adrain Cottewill 2005 Phys. Rev. D 71 064025
[5]	Berti E, Cardoso V and Casals M 2006 Phys. Rev. D 73 024013
[6]	Vitor Cardoso and Jos P S Lemos 2003 Phys. Rev. D 67 084005
[7]	Ezra T Newman 2010 “NP Stokes Fields for Radio Astronomy”, arXiv/: 1007.4351v1 [gr-qc]
[8]	Adrian C Ottewill and Elizabeth Winstanley 2000 Phys. Rev. D 62 084018
[9]	Misao Sasaki and Hideyuki Tagoshi 2003 “Analytic Black Hole Perturbation Approach to Gravitational Radiation”, arXiv/: gr-qc/0306120v1
[10]	Tian G H 2005 Chin. Phys. Lett. 22 3013
[11]	Tian G H and Zhong S Q 2009 “Solve Spheroidal Wave Functions by SUSY Method”, arXiv/: 0906.4685v2 [gr-qc]
[12]	Tian G H and Zhong S Q 2009 “New Investigation for the Spheroidal Wave Functions”, arXiv/: 0906.4687v2 [gr-qc]
[13]	Tian G H and Zhong S Q 2010 Chin. Phys. Lett. 27 040305
[14]	Dong K, Tian G H and Sun Y 2011 Chin. Phys. B 20 071101
[15]	Sun Y, Tian G H and Dong K 2011 Chin. Phys. B 20 061101
[16]	Li K, Sun Y, Tian G H and Tang W L 2011 Sci. Chin. G 41 729 (in Chinese)
[17]	Tian G H 2010 Chin. Phys. Lett. 27 030308
[18]	Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 267

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 18

相关文章 7

Metrics

本文评价

推荐阅读 0

[1]	Hong Wang(王虹), Yue Qin(秦悦), Jingxu Ma(马晶旭), Heng Shen(申恒), Ying Hu(胡颖), and Xiaojun Jia(贾晓军). Application of non-Hermitian Hamiltonian model in open quantum optical systems[J]. 中国物理B, 2021, 30(5): 50301-050301.
[2]	李芳昱, 文毫, 方祯云. High-frequency gravitational waves having large spectral densities and their electromagnetic response[J]. 中国物理B, 2013, 22(12): 120402-120402.
[3]	M. Sharif, M. Azama. The stability of a shearing viscous star with an electromagnetic field[J]. 中国物理B, 2013, 22(5): 50401-050401.
[4]	张晴,田贵花,孙越,董锟. [J]. 中国物理B, 2012, 21(4): 40402-040402.
[5]	董锟, 田贵花, 孙越. Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2[J]. 中国物理B, 2011, 20(7): 71101-071101.
[6]	孙越, 田贵花, 董锟. Spin-weighted spheroidal equation in the case of s=1[J]. 中国物理B, 2011, 20(6): 61101-061101.
[7]	宫衍香, 吴晓梅. Post-post-Newtonian deflection of light ray in multiple systems with PPN parameters[J]. 中国物理B, 2011, 20(2): 20403-020403.