2010/11/11 by Kun Dong, Dong, Kun, Guihua Tian +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #gr-qc #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1011.2579
arxiv created 2010/11/11 · arxiv updated 2010/11/12
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly studied in the paper by means of the perturbation method in supersymmetry quantum mechanics. The first-five terms of the super-potential in the series of the parameter beta are given. The general form of the nth term of the superpotential is also obtained, which could derived from the previous terms Wk, k<n. From the results, it is easy to give the ground eigenfunction of the equation. Furthermore, the shape-invariance property is investigated in the series form of the parameter beta and is proven kept in this series form for the equations. This nice property guarantee one could obtain the excited eigenfunctions in the series form from the ground eigenfunctions by the method in supersymmetry quantum mechanics. This shows the perturbation method method in supersymmetry quantum mechanics could solve the spin-weight spheroidal wave equations completely in the series form of the small parameter beta.