Relations between hyperspherical harmonic transformations and generalized Talmi–Moshinsky transformations

The correlations between the hyperspherical harmonic transformations and the generalized Talmi–Moshinsky transformations are studied for the three‐body and four‐body systems. An optical approach for solving few‐body problems through diagonalizing the Hamiltonian of a system in an optimal subset of t...

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Bibliographic Details
Published in:Journal of mathematical physics 1990-07, Vol.31 (7), p.1621-1626
Main Author: Liu, Xian‐hui
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
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Summary:The correlations between the hyperspherical harmonic transformations and the generalized Talmi–Moshinsky transformations are studied for the three‐body and four‐body systems. An optical approach for solving few‐body problems through diagonalizing the Hamiltonian of a system in an optimal subset of the basis functions of harmonic oscillators in hyperspherical coordinates is proposed. The evaluations of the interaction matrix elements are achieved with the aid of the transformation properties of hyperspherical harmonics.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.528705