  It is shown that weight operator of a composite quantum body in a weak
external gravitational field in the post-Newtonian approximation of the General
Relativity does not commute with its energy operator, taken in the absence of
the field. Nevertheless, the weak equivalence between the expectations values
of weight and energy is shown to survive at a macroscopic level for stationary
quantum states for the simplest composite quantum body - a hydrogen atom.
Breakdown of the weak equivalence between weight 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 field with constant velocity, using spacecraft or
satellite. For superpositions of stationary quantum states, a breakdown of the
above mentioned equivalence at a macroscopic level leads to time dependent
oscillations of the expectation values of weight, where the equivalence
restores after averaging over time procedure.
