ANALYTIC SOLUTION FOR THE DISSIPATIVE ANHARMONIC QUANTUM OSCILLATOR AND SEMICLASSICAL ANALYSIS

The analytic solution of the time evolution of a dissipative nonlinear quantum oscillator in the generalized s-ordered representation is der ived. The analytical solution allows for comparsion of the various rep resentations with the classical and semiclassical dynamics. It is show n by the eigenvalue analysis of the evolution operators that in the ca se of a small nonlinearity a semiclassical analysis is an excellent ap proximation to the exact quantum dynamics. This is further demonstrate d by using the Green's function of the anharmonic oscillator to solve the initial-value problem for a superposition of coherent states.