A Theory of Quantum Jumps

Abstract

Using the principles of the so-called ETH-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to \(\infty \) we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps representing a quantum-mechanical analogue of the Wiener measure on Brownian paths in the theory of diffusion.