☆ 4.7 Article

Solving the Schroedinger equation using Smolyak interpolants

JOURNAL OF CHEMICAL PHYSICS (2013)

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JOURNAL OF CHEMICAL PHYSICS
卷 139, 期 13, 页码 -

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AMER INST PHYSICS
DOI: 10.1063/1.4821348

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Chemistry, Physical Physics, Atomic, Molecular & Chemical

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  1. Natural Sciences and Engineering Research Council of Canada

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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. (C) 2013 AIP Publishing LLC.

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