Ci. Um et al., QUANTUM ANALYSIS OF THE SUSCEPTIBILITY FOR IDENTICAL ATOMS SUBJECTED TO AN EXTERNAL FORCE WITH A TAIL, Physical review. A, 54(4), 1996, pp. 2707-2713
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.