Generalized discrete variable approximation in quantum mechanics

The formal definition of the generalized discrete variable representation (DVR) for quantum mechanics and its connection to the usual variational basis representation (VBR) is given. Using the one dimensional Morse oscillator example, we compare the ‘‘Gaussian quadrature’’ DVR, more general DVR’s, a...

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Bibliographic Details
Published in:The Journal of chemical physics 1985-02, Vol.82 (3), p.1400-1409
Main Authors: LIGHT, J. C, HAMILTON, I. P, LILL, J. V
Format: Article
Language:English
Subjects:
Atomic and molecular physics
Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
Electronic structure of atoms, molecules and their ions: theory
Exact sciences and technology
Physics
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Summary:The formal definition of the generalized discrete variable representation (DVR) for quantum mechanics and its connection to the usual variational basis representation (VBR) is given. Using the one dimensional Morse oscillator example, we compare the ‘‘Gaussian quadrature’’ DVR, more general DVR’s, and other ‘‘pointwise’’ representations such as the finite difference method and a Simpson’s rule quadrature. The DVR is shown to be accurate in itself, and an efficient representation for optimizing basis set parameters. Extensions to multidimensional problems are discussed.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.448462