Abstract: A velocity-dependent quantum forced an harmonic cscillator is studied,and its exact solution is obtained by adopting the iteration mothod and the integral operators.The studyis carried on in operational form via the raising and lowering operators of the oseillator.The time developnment of the displacement and momentum operators of the quantum anharmonic osoillator is presented in shape of a Laplace transform and a subsequent inverse Laplace transform of suitable functionals.