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

作　　者：董锟 田贵花 孙越 

机构地区：[1]School of Science,Beijing University of Posts and Telecommunications

出　　处：《Chinese Physics B》2011年第7期123-132,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant Nos.10875018 and 10773002)

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 Wk, 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.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 Wk, 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.

关 键 词：spheroidal wave equation supersymmetric quantum mechanics SUPERPOTENTIAL shape invariance 

分 类 号：O413.1[理学—理论物理]