Abstract: The dispersion law of a one-dimensional diatomic lattice with on-site potential is analyzed under the harmonic approximation. With nonzero on-site potential, the frequency of acoustic branch at the center of Brillioun zone is nonzero, and the frequency increases with the on-site potential increasing. From the anticontinuous limit （AC limit） with only the on-site potential, as the on-site potential decreases and the interatomic coupling increases, the frequencies change continuously to form the two （acoustic and optical） bands and we retrieve the well-known dispersion law for the diatomic lattice.

Key words: one-dimensional diatomic lattice, dispersion law, on-site potential, AC limit