Abstract: The motion of microscopic particle in a periodic potential is an important content in the teaching of quantum mechanics and solid state physics. Based on the defective Dirac comb model, this paper studies the energy spectrum structure and typical characteristics of the wave packet scattering in the periodic potential, which can be used as an extension content in the teaching of quantum mechanics, so as to help students establish clear physical picture in the subsequent study of solid state physics.

Key words: defective Dirac comb, transfer matrix, wave packet scattering