## An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the schroedinger 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 fulfilling, a priori, the box boundary conditions. We further extend the Chebyshev approximation tomore »