For one-dimensional damping harmonic oscillator,using the technique of intergration within an ordered product of operators,the time-evolution state of this timedependent system is derived,which turns out to be a squeezed state.
The design of squeezing by a time-dependent harmonic oscillator is considered. The predetermined general time-dependent squeezing transformations are taken as the starting point from which the time evolution operator U(t,0) and then the corresponding time-dependent Hamiltonian are derived. The technique of integration within an ordered product of operators and the coherent-state representation are used in the intermediate derivations, where U(t,0) is obtained as an operator image of the classical symplectic transformation in phase space by a phase-space integral over coherent states.