An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the schroedinger equation on a grid
- Univ. of South Africa, Pretoria (South Africa)
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 to treat general functions of -matrices, thus allowing its application to cases for which no analytical expressions of the expansion coefficients are available. 23 refs., 2 figs., 6 tabs.
- OSTI ID:
- 447032
- Journal Information:
- Journal of Computational Physics, Vol. 126, Issue 2; Other Information: PBD: Jul 1996
- Country of Publication:
- United States
- Language:
- English
Similar Records
A Chebyshev polynomial interval-searching method (Lanczos economization) for solving a nonlinear equation with application to the nonlinear Eigenvalue problem
High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations