摘要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.
Abstract：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.
TIAN Gui-Hua. A New Method to Solve the Spheroidal Wave Equations[J]. 中国物理快报, 2010, 27(3): 30308-030308.
TIAN Gui-Hua. A New Method to Solve the Spheroidal Wave Equations. Chin. Phys. Lett., 2010, 27(3): 30308-030308.
[1] Flammer C 1956 Spheroidal Wave Functions (Stanford, CA: Stanford University) [2] Stratton J A, Morse J P M, Chu L J, Little J D C and Corbato F J 1956 Spheroidal Wave Functions (New York: John Wiley and Sons Inc.) [3] Li L W, Kang X K and Leong M S 2002 Spheroidal Wave Functions in Electromagnetic Theory (New York: John Wiley and Sons, Inc.) [4] Slepian D and Pollak H O 1961 Bell. Syst. Tech. J 40 43 [5] Cooper F, Khare A and Sukhatme U 1995 Phys. Rep. 251 268 and references therein [6] Khare A and Sukhatme U 1988 J. Phys. A 21 L501 [7] Tian G H and Zhong S Q 2009 Arxiv: 0906.4685,V2; 0906.4685,V3; 0906.4687,V3 [8] Tang W L and Tian G H 2009 Solving the Spheroidal Vave Equation with Small $c$ by the SUSYQM Method (preprint) [9] Gradsbteyn I S and Ryzbik L M 2000 Table of Integrals, Series, and Products 6th edn (Singapore: Elsevier)
2010, Vol. 27 
