Abstract
An algorithm for the construction of non-spurious harmonic oscillator wave functions with arbitrary permutational symmetry is presented. The harmonic oscillator wave 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. A procedure is developed to transform the resultant harmonic oscillator states from Jacobi into single particle coordinates. The procedures proposed are expected to enhance the effectiveness of many-body computations involving harmonic oscillator basis sets.
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