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

Abstract

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 $A{\rho }^{2\zeta -2}-B{\rho }^{\zeta -2}$. We show that in these cases the non-compact (compact) algebra corresponds to so(2,1) (su(2)).

References in corpus (1)

• SUSY approach to Pauli Hamiltonians with an axial symmetry

Cited by in corpus (3)

• $SU(1,1)$ solution for the Dunkl oscillator in two dimensions and its coherent states
• The su(1,1) Dynamical Algebra for the Generalized MICZ-Kepler Problem from the Schrödinger Factorization
• The su(1,1) dynamical algebra from the Schrödinger ladder operators for N-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator