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

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.

Keywords: spheroidal wave equation supersymmetric quantum mechanics super-potential eigenvalue and eigenfunction

Received: 14 September 2011
Revised: 17 October 2011
Accepted manuscript online:

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

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

Corresponding Authors: Sun Yue, E-mail:sunyue1101@126.com
E-mail: sunyue1101@126.com

Cite this article:

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 2012 Chin. Phys. B 21 040401

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

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