Equivalence of the quantum harmonic oscillator and the classical oscillator subject to a random force.

We show that the Schrodinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics of a classical harmonic oscillator subject to a random force for time intervals $O(m/\hbar)$. Conversely every solution to the Schrodinger equation arises this way. In other words the quantum harmonic oscillator is approximately nothing but the classical harmonic oscillator with the same mass and frequency subject to a random force.