  The quantization of the transverse motion energy in the continuous potentials
of atomic strings and planes can take place under passage of fast charged
particles through crystals. The energy levels for electron moving in axial
channeling regime in a system of parallel atomic strings (for instance, [110]
strings of a silicon crystal) are found in this work for the electron energy of
order of several tens of MeV, when a total number of energy levels becomes
large (up to several hundreds). High resolution of the spectral method used for
energy level search has been demonstrated. Hence this method could be useful
for investigation of quantum chaos problem.
