Non-spurious harmonic oscillator states with arbitrary permutational symmetry

Abstract

An algorithm for the construction of non-spurious harmonic oscillator (h.o.) wave functions with arbitrary permutational symmetry is presented. The h.o. wave functions, expressed in Jacobi coordinates, are calculated recursively using a new type of h.o. 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 h.o. brackets. A procedure is developed to transform the resultant h.o. states from Jacobi into single particle coordinates. The procedures proposed are expected to enhance the effectiveness of computations involving h.o. basis sets.