Exact diagonalization of two quantum models for the damped harmonic oscillator - art. no. 022107

The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has give n rise to some approximations whose validity and relation to more refined d escriptions deserve a thorough investigation. In this work, we apply a meth od that allows us to diagonalize exactly the dissipative Hamiltonians that are frequently adopted in the literature. Using this method, we derive the conditions of validity of the rotating-wave approximation (RWA) and show ho w this approximate description relates to more general ones. We also show t hat the existence of dissipative coherent states is intimately related to t he RWA. Finally, through the evaluation of the dynamics of the damped oscil lator, we notice an important property of the dissipative model that has no t been properly accounted for in previous works, namely the necessity of ne w constraints to the application of the factorizable initial conditions.