Existence of a constant stationary solution for the hydrogen atom problem in stochastic electrodynamics

Abstract

It is shown that the (approximate) Fokker-Planck equation corresponding to the hydrogen atom problem in Stochastic Electrodynamics (SED) has a trivial solution, namely the constant function. This result depends only on the drift coefficient, and therefore holds whatever the diffusion matrix. This property is related with the non-recurrence property proven recently, and the physical consequences are discussed: some drastic changes with respect to SED in its present state would be necessary for getting physically reasonable results.