  We analyze and clarify how the SGA (spectrum generating algebra) method has
been applied to different potentials. We emphasize that each energy level
$E_\nu$ obtained originally by Morse belongs to a {\em different} ${\mathfrak
{so}}(2,1)$ multiplet. The corresponding wavefunctions $\Psi_\nu$ are
eigenfuntions of the compact generators $J^\nu_0$ with the same eigenvalue
$k_0$, but with different eigenvalues $q_\nu$ of the Casimir operators $Q$. We
derive a general expression for all effective potentials which have
$\Psi_{\lambda_\nu,\nu+m}(r) \propto (J_+^\nu)^m ~\Psi_{\lambda_\nu,\nu}(r)$ as
eigenfunctions, without using super-symmetry formalism. The different actions
of SGA is further illustrated by two diagrams.
