| Calculating multidimensional discrete variable representations from cubature formulas. | |
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MedLine Citation:
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PMID: 16623468 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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Finding multidimensional nondirect product discrete variable representations (DVRs) of Hamiltonian operators is one of the long standing challenges in computational quantum mechanics. The concept of a "DVR set" was introduced as a general framework for treating this problem by R. G. Littlejohn, M. Cargo, T. Carrington, Jr., K. A. Mitchell, and B. Poirier (J. Chem. Phys. 2002, 116, 8691). We present a general solution of the problem of calculating multidimensional DVR sets whose points are those of a known cubature formula. As an illustration, we calculate several new nondirect product cubature DVRs on the plane and on the sphere with up to 110 points. We also discuss simple and potentially very useful finite basis representations (FBRs), based on general (nonproduct) cubatures. Connections are drawn to a novel view on cubature presented by I. Degani, J. Schiff, and D. J. Tannor (Num. Math. 2005, 101, 479), in which commuting extensions of coordinate matrices play a central role. Our construction of DVR sets answers a problem left unresolved in the latter paper, namely, the problem of interpreting as function spaces the vector spaces on which commuting extensions act. |
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Authors:
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Ilan Degani; David J Tannor |
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Publication Detail:
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Type: Journal Article |
Journal Detail:
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Title: The journal of physical chemistry. A Volume: 110 ISSN: 1089-5639 ISO Abbreviation: J Phys Chem A Publication Date: 2006 Apr |
Date Detail:
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Created Date: 2006-04-20 Completed Date: 2007-07-16 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9890903 Medline TA: J Phys Chem A Country: United States |
Other Details:
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Languages: eng Pagination: 5395-410 Citation Subset: - |
Affiliation:
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Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel. ilan.degani@weizmann.ac.il |
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