# Coulomb expectation values in D=3 and D=3−2ε dimensions

@article{Adkins2020CoulombEV,
title={Coulomb expectation values in
D=3
and
D=3−2$\epsilon$
dimensions},
author={Gregory S. Adkins and Md F. Alam and Conor Larison and Ruosi Sun},
journal={Physical Review A},
year={2020}
}
• Published 7 August 2019
• Materials Science, Mathematics
• Physical Review A
We explore the quantum Coulomb problem for two-body bound states, in $D=3$ and $D=3\ensuremath{-}2\ensuremath{\epsilon}$ dimensions, in detail, and give an extensive list of expectation values that arise in the evaluation of QED corrections to bound-state energies. We describe the techniques used to obtain these expectation values and give general formulas for the evaluation of integrals involving associated Laguerre polynomials. In addition, we give formulas for the evaluation of integrals…
3 Citations

## Figures from this paper

Multidimensional hydrogenic states: position and momentum expectation values
• Physics
• 2020
The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values ⟨r α ⟩ and pα , respectively. These quantities,
Calculation of higher order corrections to positronium energy levels
• Physics
Proceedings of International Conference on Precision Physics and Fundamental Physical Constants — PoS(FFK2019)
• 2019
We report on progress in the calculation of corrections to positronium energy levels of order m α 7 . Corrections at this level will be needed for the interpretation of the results of upcoming
Solutions of Pauli–Dirac equation in terms of Laguerre polynomials within perturbative scheme
• A. Arda
• Mathematics
• 2021
We search for first- and second-order corrections to the energy levels of the Pauli–Dirac equation within the Rayleigh–Schrödinger theory. We use some identities satisfied by the associated Laguerre

## References

SHOWING 1-10 OF 98 REFERENCES
O(mα6)corrections to energy levels of positronium with nonvanishing orbital angular momentum
A detailed calculation of the $O(m{\ensuremath{\alpha}}^{6})$ corrections to the energy levels of positronium for the orbital angular momentum number $lg0$ is presented. The formulas obtained are in
Nonrelativistic QED approach to the Lamb shift
• Physics
• 2005
We calculate the one- and two-loop corrections of order $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{6}$ and ${\ensuremath{\alpha}}^{2}{(Z\ensuremath{\alpha})}^{6}$, respectively, to the Lamb shift
NRQED Lagrangian at order $1/M^4$
• Physics
• 2013
The parity and time-reversal invariant effective lagrangian for a heavy fermion interacting with an abelian gauge field, i.e., NRQED, is constructed through order $1/M^4$. The implementation of
Mean values of powers of the radius for hydrogenic electron orbits
The general formulas available in the literature for calculating the time average of powers of the orbital radius of the electron in hydrogenic atoms or ions, $〈{r}^{s}〉$, are of a degree about twice
A New Method of Calculating the Mean Value of 1/rFormula for Keplerian Systems in Quantum Mechanics
The usual method of calculating the diagonal matrix elements of an integral power of the radius r in an inverse square quantum system is that due to Waller. His procedure is based on the Schrodinger
ANALYTICAL FORMULAS FOR THE EIGENVALUES AND EIGENFUNCTIONS OF A D-DIMENSIONAL HYDROGEN ATOM WITH A POTENTIAL DEFINED BY GAUSS' LAW
The solution of the Schroedinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss` law has been studied by the shifted l/d method and the {delta} expansion.
A hydrogenic atom in d‐dimensions
• Physics
• 1990
The laws of physics in d spatial dimensions are interesting and often lead to insights concerning the laws of physics in three spatial dimensions. A hydrogenic bound system in d‐dimensions is
The Momentum Distribution in Hydrogen-Like Atoms
• Materials Science, Mathematics
• 1929
The probability density that an electron have certain momenta is given by the square of the absolute magnitude of a momentum eigenfunction \${\ensuremath{\Upsilon}}_{\mathrm{nlm}}(P,