  In the Elliott SU(3) symmetry scheme the single particle basis is derived
from the isotropic harmonic oscillator Hamiltonian in the Cartesian coordinate
system. These states are transformed into the solutions of the same Hamiltonian
within the spherical coordinate system. Then the spin-orbit coupling can be
added in a straightforward way. The outcome is a transformation between the
Elliott single particle basis and the spherical shell model space.
