Classical versus quantum calculation of radiative electric quadrupole transition rates for hydrogenic states

Abstract

The semiclassical Kepler-Coulomb problem and the quantum-mechanical Schrödinger-Coulomb problem are compared for their predictions of quadrupole E2 transitions. The semiclassical treatment involves an extension of previous work for the electric dipole transitions (Physical Review A 71, 020501), and rates are derived for $\Delta \ell =0,\pm 2$ transitions on the basis of the multipolar properties of the emitted radiation. For the quantum case a derivation is presented within the Schrödinger framework without reference to spin. Comparison of the E2 rates shows reasonable agreement, but not as good as was found for the electric dipole case.

arXiv comment19 pages

References in corpus (6)

• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• A tabulation of the bound-state energies of atomic hydrogen
• The quantum emission spectra of rapidly-rotating Kerr black holes: discrete or continuous?
• Radiation of the electromagnetic field beyond the dipole approximation
• Natural broadening in the quantum emission spectra of higher-dimensional Schwarzschild black holes
• Classical calculation of radiative decay rates of hydrogenic Stark states