Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

doi:10.1088/1674-1056/20/1/010304

Abstract The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Keywords: spheroidal wave equation the perturbation method in supersymmetric quantum mechanics super-potential eigenvalue and eigenfunction

Revised: 15 September 2010
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	02.30.Gp	(Special functions)
	11.30.Pb	(Supersymmetry)

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

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Tang Wen-Lin(唐文林) and Tian Gui-Hua(田贵花) Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method 2011 Chin. Phys. B 20 010304

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[2]	Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2 Sun Yue(孙越), Tian Gui-Hua(田贵花), and Dong Kun(董锟) . Chin. Phys. B, 2012, 21(4): 040401.
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[4]	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). Chin. Phys. B, 2011, 20(7): 071101.
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[6]	Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies Tang Wen-Lin (唐文林), Tian Gui-Hua (田贵花). Chin. Phys. B, 2011, 20(5): 050301.

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Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

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