An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrodinger equation on a grid

A grid method for obtaining eigensolutions of bound systems is presented. In this, the block-lanczos method is applied to a Chebyshev approximation of exp(-H/Delta), where Delta is the range of eigenvalues we are interested in. With this choice a preferential convergence of the eigenvectors corresponding to low-lying eigenvalues of H is achieved. The method is used to solve a variety of one-, two-, and three-dimensional problems, To apply the kinetic energy operator we use the fast sine transform instead of the fast Fourier transform, thus fullfilling, a priori, the box boundary conditions. We further extend the Chebyshev approximation to treat general functions of matrices, thus allowing its application to cases for which no analytical expressions of the expansion coefficients are available. (C) 1996 Academic Press, Inc.