Basis functions for investigating collective motions of nuclei

A general solution of the Sehrödinger equation is obtained for a multidimensional oscillator in collective variables, and on this basis a method is proposed for constructing a complete basis for expanding the wave function of a nucleus in an internal coordinate system. A method is given for calculating the matrices of physical operators in the proposed basis, and the symmetry properties of the basis functions with respect to the choice of the internal axes are considered.