Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

doi:10.1088/1674-1056/20/7/071101

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 71101-071101.doi: 10.1088/1674-1056/20/7/071101

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

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

董锟, 田贵花, 孙越

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

收稿日期:2010-12-20 修回日期:2011-03-08 出版日期:2011-07-15 发布日期:2011-07-15

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

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

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

Received:2010-12-20 Revised:2011-03-08 Online:2011-07-15 Published:2011-07-15

摘要/Abstract

摘要： The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics. The first-five terms of the superpotential in the series of parameter β are given. The general form for the n-th term of the superpotential is also obtained, which could also be derived from the previous terms W_k, k < n. From these results, it is easy to obtain the ground eigenfunction of the equation. Furthermore, the shape-invariance property in the series of parameter β is investigated and is proven to be kept. This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics. We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.

Abstract: The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics. The first-five terms of the superpotential in the series of parameter β are given. The general form for the n-th term of the superpotential is also obtained, which could also be derived from the previous terms W_k, k < n. From these results, it is easy to obtain the ground eigenfunction of the equation. Furthermore, the shape-invariance property in the series of parameter β is investigated and is proven to be kept. This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics. We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.

Key words: spheroidal wave equation, supersymmetric quantum mechanics, superpotential, shape invariance

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)

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.

Dong Kun(董锟), Tian Gui-Hua(田贵花), and Sun Yue(孙越). Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2[J]. Chin. Phys. B, 2011, 20(7): 71101-071101.

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Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

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