Abstract: The one - dimensional finite symmetric square potential well model is studied by using the basis expansion method. The results are in agreement well with those obtained ones by solving the Schrdinger equation in the coordinate representation. The calculation is a good illustration of the basis expansion method in the quantum mechanics and provides a good example for teaching and studying of the method. In addition，numerical evaluation of the results also provides a good reference for teaching and studying of solving quantum problems by using computers.

Key words: one-dimensional finite symmetric square potential well model, basis expansion method, harmonic oscillator eigenfunction, matrix representation of operator