Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator.

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases. ∗Electronic address: [email protected] †Electronic address: [email protected] ‡Present Address: Department of Physics Education, Seoul National University, Seoul, 151-742, Korea. Electronic address: [email protected] 1