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

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

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.

Keywords: spheroidal wave equation supersymmetric quantum mechanics superpotential shape invariance

Received: 20 December 2010
Revised: 08 March 2011
Accepted manuscript online:

PACS:	11.30.Pb	(Supersymmetry)
	04.25.Nx	(Post-Newtonian approximation; perturbation theory; related Approximations)
	03.65.Ge	(Solutions of wave equations: bound states)
	02.30.Gp	(Special functions)

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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 2011 Chin. Phys. B 20 071101

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

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