Coherent states and dissipative systems

We study a many-body system consisting of a central harmonic oscillator linearly coupled to a reservoir of a large number of oscillators. To get the quantal description of the central oscillator we use normal-ordering operators and the coherent-state representation in order to solve the Schrödinger equation for the complete system. Then, it is shown that the wave function for the total system allows one to obtain the following results: (i) The expectation value of the coordinate of the central oscillator is the same as the classical solution for the damped harmonic oscillator and (ii) the energy of the central oscillator decays towards the correct zero-point energy.