### Abstract

It has been shown that an approximately band-limited function can be reconstructed by using the function's values taken at appropriate equidistant grid points and a generalized Hermite-contracted-continuous-distributed-approximating-function (Hermite-CCDAF) as the reconstruction function. A sampling theorem prescribing the possible choices of grid spacing and DAF parameters has been derived and discussed, and discretized-Hermite-contracted DAFs have been introduced. At certain values of its parameters the generalized Hermite-CCDAF is identical to the Shannon-Gabor-wavelet-DAF (SGWDAF). Simple expressions for constructing the matrix of a vibrational Hamiltonian in the discretized-Hermite-contracted DAF approximation have been given. As a special case the matrix elements corresponding to sinc-DVR (discrete variational representation) are recovered. The usefulness and properties of sinc-DVR and discretized-Hermite-contracted-DAF (or SGWDAF) in bound state calculations have been compared by solving the eigenvalue problem of a number of one- and two-dimensional Hamiltonians. It has been found that if one requires that the same number of energy levels be computed with an error less than or equal to a given value, the SGWDAF method with thresholding is faster than the standard sinc-DVR method. The results obtained with the Barbanis Hamiltonian are described and discussed in detail.

Original language | English |
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Pages (from-to) | 72-79 |

Number of pages | 8 |

Journal | Journal of Chemical Physics |

Volume | 110 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1999 |

### ASJC Scopus subject areas

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

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## Cite this

*Journal of Chemical Physics*,

*110*(1), 72-79. https://doi.org/10.1063/1.478086