Self-Interaction Corrections in a Nonrelativistic Stochastic Theory of Quantum Mechanics

Abstract

The radiation damping terms of classical electrodynamics are introduced into a set of stochastic equations of nonrelativistic quantum mechanics to study their effects on the energy levels of a stationary system to first order in perturbation theory. In the potential case there appear correction terms to Schr\odinger's equation, one of which is calculated by solving a subsidiary equation. In particular, we obtain for the Lamb shift an expression of essentially stochastic origin, whose structure is in complete agreement with known results. According to this calculation, which has the advantage of being devoid of divergence problems, the non-relativistic spinless contribution to the Lamb shift of the $2s$ level amounts of 60% of the total effect.