  An oscillatory term is found in both the energy expectation and dynamics of a
wave-packet in a time-varying harmonic trap and infinite potential well. They
are proved to oscillate in coherence with the time lapse within each period
depending on both the cutoff in transition energies and the specific route via
which the potential is being varied. This oscillatory term is general to
arbitrary potential forms since it derives from the interference between
crossed transition trajectories. Close analogy is made to the
Ruderman-Kittel-Kasuya-Yosida interaction for giant-magnetoresistance
trilayers, where many-body quantum interference among scattering states renders
the oscillation as a function of spacer width. This connection reveals the
generality of quantum friction due to parasitic oscillations.
