Spin-weighted spheroidal equation in the case of s=1

doi:10.1088/1674-1056/20/6/061101

中国物理B ›› 2011, Vol. 20 ›› Issue (6): 61101-061101.doi: 10.1088/1674-1056/20/6/061101

• THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS • 上一篇下一篇

Spin-weighted spheroidal equation in the case of s=1

孙越, 田贵花, 董锟

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

收稿日期:2010-11-24 修回日期:2010-12-23 出版日期:2011-06-15 发布日期:2011-06-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002).

Spin-weighted spheroidal equation in the case of s=1

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:2010-11-24 Revised:2010-12-23 Online:2011-06-15 Published:2011-06-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002).

摘要/Abstract

摘要： We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s=1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen-functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.

Abstract: We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s=1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen-functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.

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

中图分类号: (Supersymmetry)

11.30.Pb

04.25.Nx (Post-Newtonian approximation; perturbation theory; related Approximations) 03.65.Ge (Solutions of wave equations: bound states) 02.30.Gp (Special functions)

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.

Sun Yue(孙越), Tian Gui-Hua(田贵花), and Dong Kun(董锟). Spin-weighted spheroidal equation in the case of s=1[J]. Chin. Phys. B, 2011, 20(6): 61101-061101.

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Spin-weighted spheroidal equation in the case of s=1

Spin-weighted spheroidal equation in the case of s=1

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