Construction of hyperspherical functions symmetrized with respect to the orthogonal and the symmetric groups

Journal Article · Thu May 01 04:00:00 EDT 1997 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1997.5673· OSTI ID:538353

Barnea, N; Novoselsky, A ^[1]

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1. The Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)

We present a general recursive algorithm for the efficient construction of N-body wave functions that belong to a given irreducible representation (irrep) of the orthogonal group and are at the same time characterized by a well-defined permutational symmetry. The main idea is to construct independently the hyperspherical functions with well defined orthogonal symmetry, and then reduce the irreps of the orthogonal group into the appropriate irreps of the symmetry group. The recursive algorithm in both groups is similar{emdash}we diagonalize the appropriate second order Casimir operator. The algorithm is applied to the hyperspherical functions, which are standard basis functions for N-body calculations. The evaluation of one and two-body matrix elements, in this basis, requires the use of the various hyperspherical coefficients, which are given in this paper. We have encoded this algorithm and found it very efficient for calculating symmetrized hyperspherical functions. We found that, in our method, the number of coefficients of fractional parentages involved is reduced drastically compared to previous methods which do not use the orthogonal group. Therefore we are able to construct the symmetrized basis functions for N-body systems that are beyond the reach of the other approaches. {copyright} 1997 Academic Press, Inc.

• OSTI ID: 538353
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 256; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGORITHMS
CASIMIR OPERATORS
COMPUTER CODES
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
MANY-BODY PROBLEM
MATRIX ELEMENTS
O GROUPS
SO GROUPS
SPHERICAL HARMONICS
SYMMETRY GROUPS
WAVE FUNCTIONS