Under consideration of quantum crystals a method for description of molecular crystals is developed. After separating the macroscopic longitudinal electromagnetic field from the COULOMB interaction the mechanical excitations of a molecular crystal are calculated. By using these mechanical excitations the quantum theoretic formulation of the linear macroscopic electrodynamics with dispersion and without absorption is given. The dispersion law of polariton modes is derived. Connections between this theory and that of the classical polariton treatment are described.