  The equivalence principle (EP), as well as Schiff's conjecture, are discussed
(en passant), and the connection between the EP and quantum mechanics is then
briefly analyzed. Two semiclassical violations of the classical equivalence
principle (CEP) but not of the weak one (WEP), i.e. Greenberger gravitational
Bohr atom and the tree-level scattering of different quantum particles by an
external weak higher-order gravitational field, are thoroughly investigated
afterwards. Next, two quantum examples of systems that agree with the WEP but
not with the CEP, namely COW experiment and free fall in a constant
gravitational field of a massive object described by its wave-function $\Psi$,
are discussed in detail. Keeping in mind that among the four examples focused
on this work only COW experiment is based on an experimental test, some
important details related to it, are presented as well.
