Discrete variable representations of differential operators

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Abstract

By making use of known properties of orthogonal polynomials the discrete variable representation (DVR) method [J. C. Light, I. P. Hamilton, and J. V. Lill, J. Chem. Phys. 82, 1400 (1985)] has been rederived. Simple analytical formulas have been obtained for the matrix elements of DVRs of differential operators which may appear in the rovibrational Hamiltonian of a molecule. DVRs corresponding to Hermite, Laguerre, generalized Laguerre, Legendre, and Jacobi polynomial bases and to the Lanczos basis for Morse oscillator, that is, to basis sets often used in calculating rovibrational energy levels, have been discussed.

Original languageEnglish
Pages (from-to)1978-1984
Number of pages7
JournalThe Journal of Chemical Physics
Volume99
Issue number3
Publication statusPublished - 1993

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differential operators
polynomials
Polynomials
Hamiltonians
hypergeometric functions
Legendre functions
Electron energy levels
Mathematical operators
energy levels
oscillators
Molecules
matrices
molecules

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Discrete variable representations of differential operators. / Szalay, V.

In: The Journal of Chemical Physics, Vol. 99, No. 3, 1993, p. 1978-1984.

Research output: Contribution to journalArticle

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