title: Solving the Schroedinger equation using Smolyak interpolants.
abstract: In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased.
authors.affiliation: Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.
authors.forename: Gustavo
authors.initials: G
authors.lastname: Avila
authors.forename: Tucker
authors.initials: T
authors.lastname: Carrington