Classical and quantum mechanics of a particle on a rotating loop

Abstract

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi-classical standpoints. Exact solutions of the Schrödinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.