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

TL;DR

This paper demonstrates how factorization methods can systematically construct symmetry generators in two-dimensional quantum systems, revealing underlying algebraic structures like so(2,1) and su(2) in specific models.

Contribution

It provides a clear, systematic approach to deriving hidden and dynamical symmetries using factorization in 2D quantum systems, including the hydrogen atom and harmonic oscillator.

Findings

Identifies so(2,1) and su(2) algebras as symmetry structures

Shows factorization method's effectiveness in symmetry construction

Applies methods to specific 2D quantum models

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)).