The quantum mechanical wavefunction of a freely falling hydrogen atom will remain unchanged to �first order in the presence of sufficiently weak tidal gravitational fields, giving rise to a form of incompressibility not seen in classical systems. The fact that the electron is in a bound state and that only discrete energy level transitions can occur causes the atom to behave differently than a classical object in an inhomogeneous gravitational field under certain circumstances. A time- dependent energy shift that is overlooked in a widely-used gauge choice will be explored, and shown to be a real physical effect through gauge invariance. Quantum incompressibility of the wavefunction governing the electron super�fluid of a Type-I superconductor will also lead to non-classical behavior in the presence of tidal gravitational �fields, via coupling between gravitational and electromagnetic �fields. Theoretical and experimental implications will be discussed.