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The spin-weighted spheroidal equation in the case of s = 1 is studied. By transforming the independent variables, we make it take the Schrdinger-like form. This Schrdinger-like equation is very interesting in itself. We investigate it by using super-symmetric quantum mechanics and obtain the ground eigenvalue and eigenfunction, which are consistent with the results previously obtained. 相似文献
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We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen- functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time. 相似文献
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In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the "excited" eigenvalues and eigenfunctions. The results are beneficial to researchers for understanding the properties of the spin-weighted spheroidal wave more deeply, especially its integrability. 相似文献
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The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions' eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of all its terms is obtained. This means that the spheroidal problem is solved completely in the way for the ground eigen-value problem. The shape invariance property is proved retained for the super-potential and subsequently all the excited eigen-value problem could be solved. The results show that the spheroidal wave equations are integrable. 相似文献
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We present new integral equations for the spin-weighted spheroidal wave functions which in turn should lead to global uniform estimates and should help in particular in the study of their dependence on the parameters. For the prolate spheroidal wavefunction with m=0, there exists the integral equation whose kernel is (sin x)/x, and the sinc function kernel (sin x)/x is of great mathematical significance. We also extend the similar sinc function kernel (sin x)/x to the case m≠0 and s≠0, which interestingly turn out as some kind of Hankel transformations. 相似文献
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Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method 下载免费PDF全文
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. 相似文献
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The stability of the Schwarzschild black hole is restudied in the Painlevé
coordinates. Using the Painlevé time coordinate to define the initial time, we
reconsider the odd perturbation and find that the Schwarzschild black hole in the
Painlevé coordinates is unstable. The Painlevé metric in this paper
corresponds to the white-hole-connected region of the Schwarzschild black hole
(r>2m) and the odd perturbation may be regarded as the angular perturbation.
Therefore, the white-hole-connected region of the Schwarzschild black hole is
unstable with respect to the rotating perturbation. 相似文献
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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 a = a^2 w^2, the ground eigenvalue and eigenfunction are obtained. The obtained ground eigenfunction is elegantly in dosed forms. These results are new and very useful for the application of the spheroidal wave functions. 相似文献