  It has long been recognized that the dynamics of linear quantum systems is
classical in the Wigner representation. Yet many conceptually important linear
problems are typically analyzed using such generally applicable techniques as
influence functionals and Bogoliubov transformations. In this Letter we point
out that the classical equations of motion provide a simpler and more intuitive
formalism for linear quantum systems. We examine the important problem of
Brownian motion in the independent oscillator model, and show that the quantum
dynamics is described directly and completely by a c-number Langevin equation.
We are also able to apply recent insights into quantum Brownian motion to show
that the classical Fokker-Planck equation is always local in time, regardless
of the spectral density of the environment.
