A model of atomic radiation

Considering a non-relativistic quantum mechanical particle in an external potential well, coupled to an infinite free quantum field, it is rigorously proved that with certain cut-offs and in the weak coupling limit, the particle decays exponentially between its bound states as predicted by perturbation theory. The existence of a 'dynamical phase transition' for a particle attracted to two widely separated potential wells and also weakly coupled to an infinite reservoir is also proved