Newton equation and Schrödinger equation for the harmonic oscillator with probability distributions in frequency

Abstract In this paper, we discuss Newton equation for the harmonic oscillator with probability distributions in frequency, where the frequency is a stochastic variable with a suitable probability distribution. A new type of Newton equation is obtained by taking the stochastic average of Newton equation with harmonic force with respect to the fluctuating frequency. This method is also applied to the Schrodinger equation with harmonic potential.