AN EFFICIENT CHEBYSHEV-LANCZOS METHOD FOR OBTAINING EIGENSOLUTIONS OFTHE SCHRODINGER-EQUATION ON A GRID

A grid method for obtaining eigensolutions of bound systems is present ed. In this, the block-lanczos method is applied to a Chebyshev approx imation of exp(-H/Delta), where Delta is the range of eigenvalues we a re interested in. With this choice a preferential convergence of the e igenvectors corresponding to low-lying eigenvalues of H is achieved. T he method is used to solve a variety of one-, two-, and three-dimensio nal problems, To apply the kinetic energy operator we use the fast sin e 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 it s application to cases for which no analytical expressions of the expa nsion coefficients are available. (C) 1996 Academic Press, Inc.