GENERALIZED LAGUERRE FUNCTIONS

Abstract

It is well known that the factorization method plays an important role in physics. As shown in previous Chapters, we have obtained the ladder operators for some important potentials with the factorization method. Recently, the factorization method has been used to study some special functions [132]. The coherent states for generalized Laguerre functions have been worked out by Jellal, where the Klauder-Perelomov, Gazeau-Klauder and Barut-Girardello coherent states have been studied by using the su(1, 1) algebra [107]. Generally speaking, the exact solutions of the quantum systems with the central physical potentials can be expressed by the associated Laguerre functions as shown in previous some of Chapters. In this Chapter we want to systematically study the dynamic group for the generalized Laguerre functions with our approach since such a study shall be important for studying the quantum systems with the central physical potentials.