Fokker-Planck equation with linear and time dependent load forces

The motion of a particle described by the Fokker-Planck equation with constant diffusion coefficient, linear force (-gamma (t) x) and time dependent load force (beta (t)) is investigated. The solution for the probability density function is obtained and it has the Gaussian form; it is described by the solution of the linear force with the translation of the position coordinate x. The constant load force preserves the stationary state of the harmonic potential system, however the time dependent load force may not preserve the stationary state of the harmonic potential system. Moreover, the n-moment and variance are also investigated. The solutions are obtained in a direct and pedagogical manner readily understandable by undergraduate and graduate students.