Solve ∂P/∂t = -∂(μP)/∂x + D∂²P/∂x² numerically. Watch probability densities evolve under drift and diffusion. Compare with Langevin particle simulations.
The Fokker-Planck equation governs probability density evolution for Itô SDEs dX=μ(X)dt+√(2D)dW. Stationary solution: P∞(x)∝exp(-V(x)/D). The Ornstein-Uhlenbeck process (harmonic well) gives an exactly solvable Gaussian that relaxes to equilibrium (Uhlenbeck-Ornstein 1930). Double-well shows metastability and Kramers escape.