The generalized discrete variable representation. An optimal design

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Abstract

The generalized discrete variable representation, as opposed to the discrete variable representation, of a Hamiltonian is such that it can give accurate eigenvalues of the Hamiltonian even if non-Gaussian quadrature points and weights are used in its construction. A new method of building up the generalized discrete variable representation of a Hamiltonian has been described and its properties have been analyzed. This new method appears to be optimal, meaning that no other design based on the same points, weights, and basis functions can be conceived which would give more accurate eigenvalues. Numerical calculations have revealed that, remarkable accuracy can be achieved even with general, non-Gaussian quadrature points and weights.

Original languageEnglish
Pages (from-to)6940-6956
Number of pages17
JournalJournal of Chemical Physics
Volume105
Issue number16
DOIs
Publication statusPublished - Jan 1 1996

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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