Sum rules for Clebsch–Gordan coefficients from group theory and Runge-Lenz-Pauli vector

Abstract

Abstract We present sum rules for Clebsch–Gordan coefficients in the framework of SO(4) group-theoretical description of the hydrogen atom. The main results are obtained using properties of the Runge-Lenz-Pauli vector, in particular expressing the matrix elements of the powers of its last component both in spherical and parabolic basis. Connections with Stark effect and diamagnetism of the hydrogen atom are outlined.