Free-Fall Time in Quantum Theory

Macroscopic objects fall to the ground at the same time when released from the same height (with zero initial velocity). Their falling duration, the free-fall time, is universal (Galileo's Pisa Tower experiment). This universality is what underlies the geometric theory of gravitation -- the General Relativity. The universality above does not hold for quantum particles. The reason is the appearance of Planck constant as a parameter of  mass-velocity-distance dimension. In this project, we will analyze the Schroedinger equation for a subatomic particle in free-fall, and try to deduce the precise source of universality breaking. We will use Fisher information on quantum probability distribution to determine under what conditions the universality is broken.