Abstract: The electronic states in the symmetric N - potential wells are studied. Based on the Schrdinger equation，the linear equations determined by the standard conditions in the case of N = 1，2，3 and 4 are solved，the energy level and wave function are accurately calculated by using Mathematica. The mechanism of the energy level splitting into energy band is exhibited.

Key words: numerical analysis;finite multiple potential wells;Schr dinger equation;energy level and wave , function, energy bands