Activated tunneling decay of metastable state: Solution of the Kramers problem

At sufficiently low friction the Fokker-Planck equation for Brownian motion in a potential well is reduced to an integral equation for the energy variable. The basic small parameter of the problem is the ratio of the temperature T to the depth U₀ of the well. Quantum tunneling effects are naturally incorporated into the calculations. An explicit solution for Kramers' problem of the lifetime of the Brownian particle in the potential well is given.