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 δ-function potential whose energy spectrum approaches that of the rigid rotator when the strength of the potential becomes large.