The Thomas–Reiche–Kuhn sum rule and the rigid rotator

Abstract

It is shown that the Thomas-Reiche-Kuhn sum rule, associated with the photoabsorption cross section from quantum systems, appears to be violated in the case of the quantized rigid rotator. The origin of the apparent violation is investigated, and its resolution is presented on the basis of a related system, i.e., a particle in a spherical ␦-function potential whose energy spectrum approaches that of the rigid rotator when the strength of the potential becomes large.

Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

“…The importance of the boundary conditions in connection with the TRI{ sum rule has been pointed out in Ref. [32].…”

The Thomas-Reiche-Kuhn sum rule for the rigid rotator

“…In section 3 we discuss the isotropic harmonic oscillator and the rigid rotator as illustrative examples. In section 4 we comment on the results of the precedent sections in relation to the discussion in [1].…”

“…Recently Hadjimichael et al [1] discussed an apparent violation of the Thomas±Reiche±Kuhn (TRK) sum rule [2] in the case of the rigid rotator. They explained a missing contribution to the sum by means of a properly chosen quantum-mechanical model that reduces to the rigid rotator in the limit of in®nite potential strength.…”

“…Although interesting, the discussion of the problem o ered in [1] may be misleading if it is not correctly interpreted. For this reason, here we give an additional approach to the problem.…”

“…For this reason, here we give an additional approach to the problem. It is our purpose to establish the conditions of validity of the TRK sum rule and to consider explicitly the appearance of degenerate states which are omitted by [1] in some cases.…”