Filter method without boundary-value condition for simultaneous calculation of eigenfunction and eigenvalue of a stationary Schrodinger equation on a grid

The paper presents a method for simultaneous computation of eigenfunction and eigenvalue of the stationary Schrodinger equation on a grid, without imposing boundary-value condition. The method is based on the filter operator, which selects the eigenfunction from wave packet at the rate comparable to delta function. The efficacy and reliability of the method are demonstrated by comparing the simulation results with analytical or numerical solutions obtained by using other methods for various boundary-value conditions. It is found that the method is robust, accurate, and reliable. Further prospect of filter method for simulation of the Schrodinger equation in higher-dimensional space will also be highlighted.