The continuum potential approximation for description of charged particle scattering in crystals is generalized to include the influence of longitudinal lattice discreteness without the assumption of its weakness. This is done in the framework of quantum mechanical approach, and the refined version of optical potential formalism is used. It is showr that the usual concept of continuum potential has a limited applicability range which, however, can be extended to cover all practical cases provided that the ordinary continuum potential is replaced by the optical potential, generally substantially different, and, in addition, the channeling particle density distribution in crystal is modified by the transverse coordinate-dependent multiplier. Those modifications include essentially quantum effects, even for ion channeling. Nevertheless such a modified description is reduced to the usual continuum model for the special case of hyperchanneled particles. The experimental consequences of the generalized description are discussed including changes of the main parameters for the orientational dependence of the close-encounter process yield, the absence of a truly random direction in a crystal, the changed intensity of secondary processes, such as radiation damage creation, in single and polycrystals. The specific features for the cases of ion channeling, low energy ion scattering, and electron (positron) channeling are outlined. The generalized optical potential formalism proposed also leads naturally to the description of the arising dynamical chaos in quantum mechanical terms. The results obtained are easily extended to the general problem of quantum chaos. The interrelation between channeling and quantum chaos is indicated.