Exact Wave Functions and Coherent States of a Damped Driven Harmonic Oscillator

摘要

For a damped oscillator forced by a time-dependent field, the exact wave function is obtained by three different methods: (i) Path-integral, (ii) Second quantization and (iii) Dynamical invariant. The explicit form of the dynamical invariant involves a solution to a corresponding auxiliary equation. The coherent states, defined as eigenstates of a new destruction operator, form a nonorthogonal, over complete set and correspond to the minimum uncertainty states. These coherent states give the exact classical motion of the damped driven harmonic oscillator. (rh)