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Non-spurious harmonic oscillator states with arbitrary symmetry

✍ Scribed by Akiva Novoselsky; Jacob Katriel

Publisher: Elsevier Science
Year: 1989
Tongue: English
Weight: 781 KB
Volume: 196
Category: Article
ISSN: 0003-4916
DOI: 10.1016/0003-4916(89)90047-x

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✦ Synopsis

An algorithm for the construction of non-spurious harmonic oscillator wave functions with arbitrary permutational symmetry is formulated by adapting a procedure recently developed for building general single shell wave functions. The harmonic oscillator functions, expressed in Jacobi coordinates, are calculated recursively using a new type of harmonic oscillator coefficients of fractional parentage. These coefficients are the eigenvectors of the two-cycle class operator of the permutation group in the appropriate basis. The matrix elements of the class operators are evaluated by using a specific version of the harmonic oscillator brackets. The significance of this procedure to atomic, molecular and nuclear physics is pointed out. The presently proposed method is expected to be computationally very efticient.

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