Abstract:  The stationarySchrödinger equation is usually solved numerically using the finite difference method and shooting method in the coordinate space. This paper employs the Fourier transform to numerically solve the stationarySchrödinger equation in the momentum space, the solving speed is greatly improved by using the fast Fourier transform algorithm, and the corresponding MATLAB numerical codes were developed. By comparing with the analytic solutions of the eigenvalues and eigenfunctions of the one-dimensional harmonic oscillator, the reliability of the method and the correctness of the codes are verified, which provides an efficient numerical algorithm for solving the stationary Schrödinger equation.

Key words: Schr?dinger equation, fast fourier transform, one-dimensional harmonic oscillator