SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems

We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential Aρ2ζ−2 − Bρζ−2. We show that in these cases the non-compact (compact) algebra corresponds to so(2, 1) (su(2)).