  It is shown that a class of approximate resonance solutions in the three-body
problem under the Newtonian gravitational force are equivalent to quantized
solutions of a modified Schr\"odinger equation for a wide range of masses that
transition between energy states. In the macroscopic scale, the resonance
solutions are shown to transition from one resonance type to another through
weak capture at one of the bodies, while in the Schr\"odinger equation, one
obtains quantized wave solutions transitioning between different energies. The
resonance transition dynamics provides a classical model of a particle moving
between different energy states in the Schr\"odinger equation. This methodology
provides a connection between celestial and quantum mechanics.
