Non-spurious harmonic oscillator states with arbitrary symmetry

Abstract

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 efficient.