I intuitively understand macroscopic vibration, but trying to understand what it means for a particle to vibrate doesn't seem to make sense from the classical understanding I have of momentum and energy. First, are particles even said to vibrate or have vibrational energy? If so, how is momentum conserved between finite intervals when, as I understand vibration, the particle could be moving in one direction at an initial time (t0) and the opposite at the final time (tf). In these cases I can see how energy, as a scalar, might be conserved, but not momentum as a vector. For context, I'm trying to develop a deeper understanding of temperature and molecular walk, which depend on the random motion of a particle, which I vaguely understand as a store of "vibrational energy."