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Chin. Phys. B, 2012, Vol. 21(4): 040401    DOI: 10.1088/1674-1056/21/4/040401
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Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

Sun Yue(孙越), Tian Gui-Hua(田贵花), and Dong Kun(董锟)
School of Science, Beijing University of Posts And Telecommunications, Beijing 100876, China
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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