In a series of articles we were able to show that the problem of finding the discrete eigenvalues and eigenstates associated to some Hamiltonians of quantum mechanics could be cast as an algebraic problem related to the Lie algebra SO(2,1). What we saw was that a specific set of differential operators satisfying the SO(2,1) commutation relations were an irreducible representation of that algebra. The spectrum of the compact generator was simply related to the eigen energies and the eigen- functions of that same compact generator were simply related to the eigenfunctions of the Hamiltonian. First in 1970 we solved some simple cases in this way, essentially the harmonic oscilator problem and the Coulomb problem. Later that same year we saw how to solve algebraically the Hamiltonian associated to Morse's short range potential case. In 1975 (with Sebastián Salamó) we solved Coulomb's problem but in the case of Dirac's equation. Much later, in two papers in 1991 and 1993 again with Sebastián Salamó, we found the alg- ebraic treatment of Schröd- inger's equation with the huge class of potentials that Natanzon had defined. The key still were the irreducible representations of SO(2,1).