Evolution of the wave function in a dissipative system

Abstract

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert spaces. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path-integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner linewidth theory follows easily.