We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schrdinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schrdinger ldblquote Coulomb propagator. Selected numerical results are presented. The full set of values is available at arXiv.org/quant-ph/0504002.
U. D. Jentschura and P. J. Mohr, "Calculation of Hydrogenic Bethe Logarithms for Rydberg States," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 72, no. 1, pp. 012110-1-012110-9, American Physical Society (APS), Jul 2005.
The definitive version is available at https://doi.org/10.1103/PhysRevA.72.012110
Keywords and Phrases
Quantum Number; Schrdinger Ldblquote Coulomb Propagator; Virtual Photon Energy; Computation Theory; Hydrogen; Numerical Analysis; Problem Solving; Quantum Theory
International Standard Serial Number (ISSN)
Article - Journal
© 2005 American Physical Society (APS), All rights reserved.