QUANTUM ANALYSIS OF THE SUSCEPTIBILITY FOR IDENTICAL ATOMS SUBJECTED TO AN EXTERNAL FORCE WITH A TAIL

Using the invariant operator method, we have analytically obtained the exact wave function, propagator, and uncertainty relations for the qu antum damped harmonic oscillator governed by a time-dependent external force with a tail characterizing the influence of the past. From thes e quantities, the frequency-dependent susceptibility, the index of ref raction, and the extinction coefficient for N identical atoms in a vol ume V are evaluated. The susceptibility satisfies the common propertie s, known as Kramers-Kronig relations, and as a given parameter that de termines the nature of the tail goes to infinity, the behaviors of the se results are exactly reduced to the ones for a classical case.