### 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 language | English |
---|---|

Pages (from-to) | 1978-1984 |

Number of pages | 7 |

Journal | The Journal of Chemical Physics |

Volume | 99 |

Issue number | 3 |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*99*(3), 1978-1984.

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

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 99, no. 3, pp. 1978-1984.

}

TY - JOUR

T1 - Discrete variable representations of differential operators

AU - Szalay, V.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001585280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001585280&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001585280

VL - 99

SP - 1978

EP - 1984

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 3

ER -