Abstract
The dynamic structure factor S(Q,ω) of the three-dimensional quantum harmonic oscillator has been known exactly as a function of momentum transfer ℏQ, energy transfer ℏω and temperature T for a very long time. One aspect of the exact solution has not been explicitly discussed so far: for large Q the maximum in S(Q,ω) is located at a frequency ω = ωM(Q,T), which is persistently lower than the commonly expected recoil frequency ωR(Q) even for Q = ∞ and increasingly so for lower T. We present a new consistent zeroth-order estimate for the frequency shifts (with respect to ωR(Q)) as found in actual (neutron) scattering experiments on condensed matter at large Q.