  We consider several models of the damped oscillators in nonrelativistic
quantum mechanics in a framework of a general approach to the dynamics of the
time-dependent Schroedinger equation with variable quadratic Hamiltonians. The
Green functions are explicitly found in terms of elementary functions and the
corresponding gauge transformations are discussed. The factorization technique
is applied to the case of a shifted harmonic oscillator. The time-evolution of
the expectation values of the energy related operators is determined for two
models of the quantum damped oscillators under consideration. The classical
equations of motion for the damped oscillations are derived for the
corresponding expectation values of the position operator.
