Regularization of central forces with damping in two and three dimensions

Abstract

Two damped, central force systems are investigated and equivalent, undamped systems are obtained. The dynamics of a particle moving in 1 r potential and subjected to a damping force is shown to be regularized a la Levi-Civita. This mapping is then elevated to the corresponding quantum mechanical systems and using it, the energy spectrum of the former is calculated. Mapping of a particle moving in a harmonic potential subjected to damping to an undamped system is then derived using Bohlin-Sudman transformation, for both classical and quantum regime.