Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates

摘要

The issue of the observability of the Lamb shift in systems withnon-degenerate energy levels is put to question. To this end, we compute theLamb shift of such systems in the electromagnetic environment provided by twoinfinite parallel conducting plates, which is instrumental in demonstrating theexistence of the so-called Casimir effect. A formula giving the relative changein the Lamb shift (as compared to the standard one in vacuum) is explicitlyobtained for spherical semiconductor Quantum Dots (QD). It is the result of acareful mathematical treatment of divergences in the calculations involvingdistribution theory, which also settles a controversy on two differentexpressions in the existing literature. It suggests a possibility of QDnon-degenerate energy spectrum fine-tuning for experimental purposes as well asa Gedankenexperiment to observe the Lamb shift in spherical semiconductorquantum dots.