Abstract: In this paper, lattice vibration of one-dimensional j-atom chain is taken as the theoretical calculation model, and its equations are obtained under the harmonic and the nearest adjacent approximation. By setting j=1, 2, and 3, respectively, the dispersion relations of one-dimensional single atom, two atoms and three atoms chain lattice vibration are derived which are the same as those in the existing textbooks and references. The results have shown that the equations of one-dimensional j-atom chain lattice vibration obtained in this paper are general. Then starting from this set of equations, the influence of typical crystal structure parameters (such as atomic distance, restoring force coefficient, and atomic mass) on the dispersion relations of one-dimensional four atoms chain lattice vibration is analyzed by numerical simulation, which intensifies the impact of related content of lattice vibration in solid-state physics, and provides a certain reference value for the fabrication of band-pass filters in engineering.

Key words: solid-state physics, one dimensional j-atom chain, lattice vibration, dispersion relation