Analytical Study of the Forced Harmonic Oscillator with Time Dependent Parameters by Means of the Invariant Dynamical Linear Operator

A general treatment of the quantum forced harmonic oscillator with time dependent mass and frequency is presented. We use the invariant dynamical linear operator method. We analyse the uncertainty principle and obtain the quantum correlation of the forced quantum harmonic oscillator with parameters depending upon time. We prove that these parameters do not depend on the external force. We evaluate the time dependent probability density; we prove that this parameter depends on the external force.