A direct relaxation method for calculating eigenfunctions and eigenvalues of the schrödinger equation on a grid

Abstract

Eigenfunctions and eigenvalues of the Schrodinger equation are determined by propagating the Schrodinger equation in imaginary time. The method is based on representing the Hamiltonian operation on a grid. The kinetic energy is calculated by the Fourier method. The propagation operator is expanded in a Chebychev series. Excited states are obtained by filtering out the lower states. Comparative examples include: eigenfunctions and eigenvalues of the Morse oscillator, the Hénon-Heiles system and weakly bound states of He on a Pt surface.