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We construct the linear and quadratic polynomial dynamical invariants for theclassical and quantum time-dependent harmonic oscillator driven by atime-dependent force. To obtain them, we use exclusively the associatedequations of motion for the system. We also find an algebraic relationshipbetween the linear and quadratic invariants at the classical and quantum level.

Construction of dynamical invariants for the time-dependent harmonic oscillator with a time-dependent driven force