A Solution of One-Dimensional Stationary Schrodinger Equation by the Fourier Transform

In this paper, a new numerical method for solving of one-dimensional stationary Schrodinger equation has been presented. The method is based on the Fourier transform of a wave equation. It is shown that, as a result we obtain an integral equation where integral is replaced by sum. A main problem is transformed in the eigenvalue/eigenvector problem which corresponds to discrete energy levels as well as the Fourier transform of wave functions. Wave function is obtained by usage of the inverse Fourier transform. Discrete energy levels are split and form the forbidden and permitted zones for the one-dimensional finite crystal. The method is tested in many examples, and it is characterized by high accuracy and stability of search of the discrete energy levels.