Abstract: In this paper, the phonon dispersion relation of lattice vibrations from one-dimension to three-dimension is solved by constructing dynamic matrix equation. Compared to traditional method of solving one-dimensional atomic chain classical model using Hamilton’s canonical equations in solid state physics courses, constructing a dynamic matrix provides a more unified and universal form for solving phonon dispersion relation from one-dimensional to three-dimensional lattice. It is helpful to establish a continuous physical picture of one-dimensional to three-dimensional lattice vibration from the way of thinking. In terms of numerically solving three-dimensional lattice vibrations and considering the effects of anharmonicity, this method also offers greater convenience.

Key words: lattice vibration, dynamic matrix equation, phonon dispersion relations