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We present sum rules for Clebsch-Gordan coefficients in the framework ofSO(4) group-theoretical description of the hydrogen atom. The main results areobtained using properties of the Runge-Lenz- Pauli vector, in particularexpressing the matrix elements of the powers of its last component both inspherical and parabolic basis. Connections with Stark effect and diamagnetismof the hydrogen atom are outlined.

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