  Time evolution of the expectation values of various dynamical operators of
the harmonic oscillator with dissipation is analitically obtained within the
framework of the Lindblad's theory for open quantum systems. We deduce the
density matrix of the damped harmonic oscillator from the solution of the
Fokker-Planck equation for the coherent state representation, obtained from the
master equation for the density operator. The Fokker-Planck equation for the
Wigner distribution function is also solved by using the Wang-Uhlenbeck method
of transforming it into a linearized partial differential equation for the
Wigner function, subject to either the Gaussian type or the $\delta$-function
type of initial conditions. The Wigner functions which we obtain are
two-dimensional Gaussians with different widths.

High Energy Physics - Theory