Using the Finite Difference Method to Solve the Energy Eigenvalue Equation

In order to investigate and develop numerical calculation method for Schrödinger equation,we apply the finite difference method to eigenvalue problems in quantum mechanics.In a Cartesian coordinate system, we carry out a finite difference analysis of a general form of the energy equation.We demonstrate this method in the case of one,two and three-dimensional isotropic harmonic oscillators,the results show that the finite difference method is quite accurate and useful.