Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

Diffusion equation with a drifting velocity term (continuous limit) of a multiurn Ehrenfest model was analyzed. A transformation was introduced for the the quantum particle problem, moving under the influence of a time varying magnetic field. It was observed that the continuous limit of the the model exists by defining the drifting velocity and diffusion constant, if the density function is defined as the continuous limit of the fraction m_i/N. It was also observed that the diffusion equation solutions are helpful in finding the wave function or Green's function of problems of time-dependent quantum mechanics.