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Title: Solving the Schroedinger equation using Smolyak interpolants

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:
;  [1]
  1. Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6 (Canada)
Publication Date:
OSTI Identifier:
22224137
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 139; Journal Issue: 13; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENFUNCTIONS; EIGENVALUES; ENERGY LEVELS; INTEGRAL EQUATIONS; INTERPOLATION; SCHROEDINGER EQUATION