Does the Equivalence between Gravitational Mass and Energy Survive for a Quantum Body?

We consider the simplest quantum composite body, a hydrogen atom, in the presence of a weak external gravitational eld. We show that passive gravitational mass operator of the atom in the post-Newtonian approximation of general relativity does not commute with its energy operator, taken in the absence of the eld. Nevertheless, the equivalence between the expectations values of passive gravitational mass and energy is shown to survive at a macroscopic level for stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level for stationary quantum states can be experimentally detected by studying unusual electromagnetic radiation, emitted by the atoms, supported and moved in the Earth gravitational eld with constant velocity, using spacecraft or satellite.