  Quantum theory is proposed of high energy electrons scattering in ultrathin
crystals. This theory is based upon a special representation of the scattering
amplitude in the form of the integral over the surface surrounding the crystal,
and on the spectral method of determination of the wave function. The
comparison is performed of quantum and classical differential scattering
cross-sections in the transitional range of crystal thicknesses, from those at
which the channeling phenomenon is not developed up to those at which it is
realized. It is shown that in this thickness range the quantum scattering
cross-section, unlike the classical one, contains sharp peaks corresponding to
some specific scattering angles, that is connected with the diffraction of the
incident plane wave onto the periodically distributed crystal atomic strings.
It is shown that the value of the scattering cross-section in the peaks varies
periodically with the change of the target thickness. We note that this must
lead to a new interference effect in radiation that is connected with the
rearrangement of incident wave packet in transitional area of crystal
thicknesses.
