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 exten...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.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10875018)the National Basic Research Program of China (Grant No. 2010CB923200)
文摘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.
