  The simplest quantum composite body, a hydrogen atom, is considered in the
presence of a weak external gravitational field. We define an operator for the
passive gravitational mass of the atom in the post-Newtonian approximation of
the general relativity and show that it does not commute with its energy
operator. Nevertheless, the equivalence between the expectation values of the
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 by and moving in the Earth's gravitational field with
constant velocity, using spacecraft or satellite

General Relativity and Quantum Cosmology