Can all the recurrence relations for spherical functions be extended to spheroidal functions  

作　　者：TIAN GuiHua LI ZhaoYang 

机构地区：[1]School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2011年第10期1775-1782,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10875018);the National Basic Research Program of China (Grant No. 2010CB923200)

摘　　要：There are two kinds of recurrence relations for the spherical functions Pml. The first are those with the same m but different l. Thesecond are those with the same l but different m. The spheroidal functions are extensions of the spherical functions. Recurrencerelations of the first kind are obtained for the spheroidal functions in recent studies. Using the shape invariance method in super-symmetric quantum mechanics, we investigate the second type of recurrence relations for the spheroidal functions. The resultsshow that the second kind of recurrence relation can not be extended to the spheroidal functions.There are two kinds of recurrence relations for the spherical functions Pml. The first are those with the same m but different l. Thesecond are those with the same l but different m. The spheroidal functions are extensions of the spherical functions. Recurrencerelations of the first kind are obtained for the spheroidal functions in recent studies. Using the shape invariance method in super-symmetric quantum mechanics, we investigate the second type of recurrence relations for the spheroidal functions. The resultsshow that the second kind of recurrence relation can not be extended to the spheroidal functions.

关 键 词：spheroidal wave functions supersymmetry quantum mechanics super-potential shape-invariance 

分 类 号：TQ424.1[化学工程] S858.291[农业科学—临床兽医学]