The course of solid physics mainly studies the relationship between the microstructure of matter and the macroscopic properties of matter. In order to express these problems quantitatively, many mathematical models need to be constructed, and all mathematical knowledge can be used to express the physical problems of solids, among which mathematical physical equations, special function theory and complex variable functions are typical. This includes the basic contents such as differential equation and Fourier transform. For example, to study the motion characteristics of electrons in a crystal in a periodic lattice requires a periodic function description, which involves a large number of Fourier transforms.