- Published 2008

As shown by Pauli, Z. Phys. 36, 336 1926 , the electric dipole operator r can be replaced by the Runge-Lenz vector A when operating within the n2 degenerate manifold of hydrogenic states of principal quantum number n. We seek to develop similar rules for higher multipole operators by expressing equivalent operators in terms only of the two vector constants of motion—the orbital angular momentum L and the Runge-Lenz vector A—appropriate to the degenerate hydrogenic shell. Equivalence of two operators means here that they yield identical matrix elements within a subspace of Hilbert space that corresponds to fixed n. Such equivalent-operator techniques permit direct algebraic calculation of perturbations of Rydberg atoms by external fields and often exact analytical results for transition probabilities. Explicit expressions for equivalent quadrupole and octupole operators are derived, examples are provided, and general aspects of the problem are discussed.

@inproceedings{Ostrovsky2008EquivalentMO,
title={Equivalent multipole operators for degenerate Rydberg states},
author={V . N . Ostrovsky and Daniel Vrinceanu and Martin Flannery},
year={2008}
}