In 1963-1990 he was Director of Institute for Theoretical Physics of the Ukrainian Academy of Sciences.

[1] His main contributions were in theory of absorption, scattering and dispersion of the light in molecular crystals.

[1] In 1973, Davydov applied the concept of molecular solitons in order to explain the mechanism of muscle contraction in animals.

[3][4][5] He studied theoretically the interaction of intramolecular excitations or excess electrons with autolocal breaking of the translational symmetry.

[6][7] In 1979, Davydov published the first textbook on quantum biology entitled "Biology and Quantum Mechanics" in Russian, which was then translated in English three years later.