Abstract
In this paper, we first roughly present the basic physical idea about quantum theory and the history of quantum theory. we will give a simple interpretation ofSchr‥odinger equation and illustrate something about quantum well. Furthermore,we investigate the one-dimensional discrete Schr‥odinger equation with Dirichletboundary conditions. In particular, the mass of a single electron in Schr‥odinger equation is represented by non-parabolic effective mass approximation. Here, we use a central-differencing method to discretize the equations with the uniform mesh size, and we will construct the characteristic equation of this modal problem.As the same skill of this paper [4], we analyze the property of these equations to find the solutions (eigenvalues) of the equations. Here, the eigenvalues andeigenvectors correspond to the energy states and wave functions of the quantum well, respectively. Finally, the aim of this paper is to find out the number of thediscrete energy states lying in the well.