Our second result is a breakdown of the equivalence between passive gravitational mass and energy at a microscopic level for stationary quantum states due to the fact that the mass operator does not commute with energy operator, taken in the absence of gravitational field.
where we introduce passive gravitational mass operator of an electron to be proportional to its weight operator in a weak centrosymmetric gravitational field (2),
9) corresponds to the bare electron mass, me, the second term corresponds to the expected electron energy contribution to the mass operator, whereas the third nontrivial term is the virial contribution to the mass operator.
9), the expectation value of the gravitational mass operator per one electron is
First of all, we recall that the mass operator (9) does not commute with electron energy operator, taken in the absence of gravitational field.