Sum rules for Clebsch-Gordan coefficients from group theory and Runge-Lenz-Pauli vector
Jean-Christophe Pain
TL;DR
This paper derives sum rules for Clebsch-Gordan coefficients using SO(4) group theory and properties of the Runge-Lenz-Pauli vector, linking algebraic methods to hydrogen atom phenomena.
Contribution
It introduces new sum rules for Clebsch-Gordan coefficients based on the group-theoretical approach involving the Runge-Lenz-Pauli vector.
Findings
Derived sum rules for Clebsch-Gordan coefficients.
Expressed matrix elements of the Runge-Lenz-Pauli vector in different bases.
Connected algebraic results to Stark effect and diamagnetism phenomena.
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.
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Taxonomy
TopicsAdvanced Chemical Physics Studies · Scientific Research and Discoveries · Atomic and Molecular Physics