Abstract: Discrete tight-binding model is a very important one in physics. It captures the essential physics process by a simple interacting Hamiltonian. In this paper, the derivation of discrete tight-binding model from the wave equation of quantum mechanics is introduced. As an example, the result is applied on two common models in Solid State Physics. The discussions  provide materials for students to study Solid State Physics further and also help students to read related scientific literature.

Key words: tight-binding model, Wannier representation, second quantization