2 COMPUTER-PROGRAMS FOR SOLVING THE SCHRODINGER-EQUATION FOR BOUND-STATE EIGENVALUES AND EIGENFUNCTIONS USING THE FOURIER GRID HAMILTONIAN METHOD

Two computer programs (FGHEVEN and FGHFFT) for solving the one-dimensional Schrodinger equation for bound-state eigenvalues and eigenfunctions are presented. Both computer programs are based on the Fourier grid Hamiltonian method (J. Chem. Phys. 91 (1989) 3571). The method is exceptionally simple and robust. It relies on using the momentum representation for the kinetic energy operator and the coordinate representation for the potential energy. The first computer program (FGHEVEN) is based on an explicit (very simple) expression for the Hamiltonian matrix. The eigenvalues of this matrix give the required bound-state energies and the eigenvectors yield directly the eigenfunctions evaluated on the regularly spaced grid points. In this paper the theory has been slightly extended to encompass the situation where an even number of grid points is used. The second program (FGHFFT) is based on a complimentary theory which makes use of the discrete fast Fourier transform technique to evaluate the Hamiltonian matrix. The programs are self-contained and include subroutines to find the eigenvalues and eigenvectors needed.