  We apply the canonical perturbation theory to the semi--quantal hamiltonian
of the SU(3) shell model. Then, we use the Einstein--Brillowin--Keller
quantization rule to obtain an analytical semi--quantal formula for the energy
levels, which is the usual semi--classical one plus quantum corrections.
Finally, a test on the numerical accuracy of the semiclassical approximation
and of its quantum corrections is performed.
