Stationary states of the semiclassical diffusion equation for a system in a blackbody radiation field

The Lorentz-Dirac equation for a nonrelativistic particle in a blackbody radiation field is solved by a stationary trial solution formed by a slowly varying part depending on the coordinate, which is supposed to be separable, plus a rapidly fluctuating part with zero average and constant variance, depending essentially on time only. Then an equation is obtained for the slowly varying part, including the stochastic field parameters, and this dependence is evaluated explicitly for special cases. The diffusion equation in coordinate space is established for this system in a general stationary state. It is shown that the condition for the probability density P(chi,t) to be representable in the same form as a quantum-mechanical pure state, is a certain relation between the diffusion coefficient in any stationary state and the value of the mean squared fluctuation of the momentum