2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92737We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level $E_ν$ obtained originally by Morse belongs to a {\em different} ${\mathfrak {so}}(2,1)$ multiplet. The corresponding wavefunctions $Ψ_ν$ are eigenfuntions of the compact generators $J^ν_0$ with the same eigenvalue $k_0$, but with different eigenvalues $q_ν$ of the Casimir operators $Q$. We derive a general expression for all effective potentials which have $Ψ_{λ_ν,ν+m}(r) \propto (J_+^ν)^m ~Ψ_{λ_ν,ν}(r)$ as eigenfunctions, without using super-symmetry formalism. The different actions of SGA is further illustrated by two diagrams.Quantum Physicstext