Coherent states and the resonance of a quantum damped oscillator

A quantum-mechanical model of a damped harmonic oscillator (both with time-independent and time-dependent parameters) is studied in the framework of the linear Schr\"odinger equation with a Hermitian nonstationary Hamiltonian. Integrals of the motion of this equation and their eigenstates, including coherent states, are constructed. The influence of an external harmonic force to the time evolution of various average values calculated over coherent states is considered, including the resonance case. The specific symmetry of the Hamiltonian leading to the new concept of loss-energy states is discussed.