On the exact solution of the harmonic quadrupole collective hamiltonian

Explicit expressions for the eigenfunctions of the harmonic quadrupole collective Hamiltonian both in the lab and intrinsic systems of references are given. Two alternative approaches, the technique of projective coherent states and the theory of harmonic polynomials in collective coordinates, are used. Symmetry properties and recursive formulae for the internally labelled wave functions are established. Applications to the yrast states as well as to the low angular momentum states in the case of the asymmetric rotor Hamiltonian are also presented. (Auth.)