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Quantum Physics Theory


Theoretical work relevant to the determination of values of the fundamental constants, tests of bound-state quantum electrodynamics (QED), and methods of numerical analysis are included among the activities of the Fundamental Constants Data Center.


The scope of the work ranges from calculations of QED effects in atoms to detailed studies of photon wave functions.

Major Accomplishments:

Photon wave functions

The fundamental building block of the theory of photons is the wave function for a single photon. A detailed study of the properties of a photon wave equation and its solutions has been made in a recent work that considers both classical and quantum solutions of the Maxwell equations. Properties that are expected to be satisfied by a photon wave function are enumerated and shown to be met by the formalism provided in the study: Solutions of the Maxwell equations and photon wave functions, P. J. Mohr, Annals of Physics 325, 607-663 (2010). (Preprint PDF)

Rydberg states

Excited states of atoms have attractive properties as a potential source of information on fundamental constants and tests of theory. It has been shown that the largest sources of uncertainty of atomic levels, namely the charge radius of the nucleus and higher-order quantum electrodynamic effects are greatly diminished in states with angular momentum 2ħ or greater. These points are discussed and results of detailed calculations, including QED effects for excited levels in hydrogen-like atoms are given in: Fundamental Constants and Tests of Theory in Rydberg States of Hydrogenlike Ions, U. D. Jentschura, P. J. Mohr, J. N. Tan, and B. J. Wundt, Phys. Rev. Lett. 100, 160404 (2008). (Reprint PDF)

Precision Frequencies

The transition frequencies in hydrogen and deuterium are among, and may actually be, the most precise quantities in physics that can be both measured and calculated. A searchable database of the theoretical predictions for these frequencies and the corresponding energy levels is available on the NIST Physics Laboratory Website. The calculated values are based on a least-squares analysis of the best available theory and experiments. This approach assures that the covariances of the levels is taken into account, with the result that the predictions in some cases have smaller relative uncertainties than the uncertainty in the Rydberg constant. The database is available at
Precise Calculation of Transition Frequencies of Hydrogen and Deuterium Based on a Least-Squares Analysis, U.D. Jentschura, S. Kotochigova, E.-O.
Le Bigot, P.J. Mohr, and B.N. Taylor, Phys. Rev. Lett. 95, 163003 (2005).(PDF)

A whimsical depiction of a photon wave packet

Lead Organizational Unit:


Peter Mohr