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 (4)

• Matrix Hamiltonians: SUSY approach to hidden symmetries
• SUSY approach to Pauli Hamiltonians with an axial symmetry
• Monopole supersymmetries and the Biedenharn operator
• Hidden supersymmetries in supersymmetric quantum mechanics

Cited by in corpus (7)

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• $SU(1,1)$ solution for the Dunkl-Coulomb problem in two dimensions and its coherent states
• Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime
• 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
• su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions
• An $su(1,1)$ algebraic approach for the relativistic Kepler-Coulomb problem