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2010•Chinese Physics LettersRequires access

Ground State Eigenfunction of Spheroidal Wave Functions

Tian Gui-Hua, Zhong Shu-Quan

Open publisher page 15 citations

Abstract

We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter α = a 2 w 2 , the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in closed forms. These results are new and very useful for the application of the spheroidal wave functions.

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What this paper is about

We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter α = a 2 w 2 , the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in closed forms. These results are new and very useful for the application of the spheroidal wave functions.

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Available abstract

We study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics. In the first three terms of parameter α = a 2 w 2 , the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in closed forms. These results are new and very useful for the application of the spheroidal wave functions.

Key concepts: Eigenfunction, Eigenvalues and eigenvectors, Wave function, Ground state, Perturbation (astronomy), Physics, Supersymmetric quantum mechanics, Quantum mechanics

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