Comment on “Induced transitions and energy of a damped oscillator”

In a recent paper Croxson [Phys. Rev. A 49, 588 (1994)] reported dissipation-induced transition probabilities from the ground state to higher states for a quantum harmonic oscillator. A partial approximate result was given for the oscillator to remain in its ground state, while for higher transitions the situation became complicated. Our approach provides an exact simple form closed expression for any order of transition. In addition, we supply the evolution of the work done by the system on its environment.