Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

The Thomas-Reiche-Kuhn sum rule for an atom of N equally spaced energy levels

C. Baxter

Published Dec 14, 1992• 9 citations
Publisher

Abstract

The Thomas-Reiche-Kuhn sum rule is determined for an atom consisting of an arbitrary number of discrete, equally spaced eigenenergy levels. This generalization is consistent with a two-level atom and with a usually seen form of the sum rule involving the atomic ground state, and resolves an apparent paradox reported elsewhere.
DOI
10.1088/0953-4075/25/23/001

Related papers

Sum Rules for Atomic Transition Probabilities

John P. Vinti

Some new sum rules for atomic transition probabilities are developed; they are similar to the well-known rule of Kuhn, Reiche, and Thomas. They give, if unpolarized light is incident on any gaseous element in any given discrete energy level, the total absorption, excitation plus ionization, with various types of frequency weighting. The results are similar to those of Dirac and Harding, but are more general in that they apply to any discrete state of any atom, rather than to the ground state of hydrogen only. The method differs from that of Dirac and Harding.

Physical Review•Aug 15, 1932•49 citations

Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Salvatore Savasta, Omar Di Stefano, Franco Nori

The Thomas-Reiche-Kuhn (TRK) sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron, and it provides an important constraint on the transitionmatrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light- matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

De Gruyter eBooks•May 25, 2021•1 citation

Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Salvatore Savasta, Omar Di Stefano, Franco Nori

Abstract The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

arXiv:2002.02139•Nanophotonics•Nov 18, 2020•17 citations

The sum rule for spectroscopic factors in the seniority scheme of identical particles

Masao Nomura

Spectroscopic factors partitioning an identical-particle state into a couple of substates with definite seniorities are summed into a simple form. This sum rule is an extension of the reduction relation for the fixed-seniority average of a many-body operator. The seniority projection operator is utilized throughout the present formulation

Journal of Mathematical Physics•Jan 1, 1987•6 citations

Sum-Rule Dynamics

T. A. Osborn, Richard Froese, S. F. Howes

A new class of sum rules in nonrelativistic scattering theory is obtained. By extending the concept of the Fredholm determinant to a local form defined at each space point $x$, a function with analytic properties analogous to the Fredholm determinant, but containing more information, is found. These rules assume the form of the power-moment problem and are valid in both quantum and classical mechanics.

Physical Review Letters•Dec 22, 1980•4 citations

Center-of-mass motion of anN-particle atom or ion and the Thomas-Reiche-Kuhn sum rule

C. Baxter

The Thomas-Reiche-Kuhn sum rule is corrected for the motion of the atomic center of mass, and generalized to include ions. The results are specialized to the case of a two-level atom or ion.Received 18 January 1994DOI:https://doi.org/10.1103/PhysRevA.50.875©1994 American Physical Society

Physical Review A•Jul 1, 1994•8 citations
Some new sum rules for atomic transition probabilities are developed; they are similar to the well-known rule of Kuhn, Reiche, and Thomas. They give, if unpolarized light is incident on any gaseous element in any given discrete energy level, the total absorption, excitation plus ionization, with various types of frequency weighting. The results are similar to those of Dirac and Harding, but are more general in that they apply to any discrete state of any atom, rather than to the ground state of hydrogen only. The method differs from that of Dirac and Harding.
The Thomas-Reiche-Kuhn (TRK) sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron, and it provides an important constraint on the transitionmatrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light- matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.
Abstract The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.
A new class of sum rules in nonrelativistic scattering theory is obtained. By extending the concept of the Fredholm determinant to a local form defined at each space point xxx, a function with analytic properties analogous to the Fredholm determinant, but containing more information, is found. These rules assume the form of the power-moment problem and are valid in both quantum and classical mechanics.