It is a partial differential equation very much like the wave equation for the explanation of sound, radio and light waves, etc.But in many-body systems quantum mechanics goes way beyond our familiar kind of wave phenomena.These two phenomena contradict our expectations because we try to find a simple explanation for the behavior of many interesting and useful objects.
This bridge provides a transition from QM to CM, as well as from CM to QM.
Very surprisingly, the movement of a small particle like the electron in a molecule looks more like a wave on the surface of a pond than the scratch of a dot on some plate.
Wave phenomena of this kind describe the propagation of light, and quite generally most electronagnetism, as well as sounds in any kind of medium.
It is based on the solution of ordinary differential equations.
They are able to explain what we now call chaos, although finding the best methods for each case is not easy.