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.
基金
supported by the National Natural Science Foundation of China (Grant No. 10875018)
the National Basic Research Program of China (Grant No. 2010CB923200)
关键词
球状
复发
球形
超对称量子力学
变性方法
PML
spheroidal wave functions, supersymmetry quantum mechanics, super-potential, shape-invariance
