To further connect the classical autocorrelation functions with the quantum autocorrelation functions for excited states absorptions, here we consider a special ensemble for the harmonic oscillator, in which the ground state is not occupied whereas the excited state are occupied according to the Boltzmann distribution. In this special ensemble, since the ground state is not occupied, the quantum autocorrelation function contains information of excited states absorptions (mainly 1 → 2) but no fundamental transition. The position autocorrelation function can be computed analytically: