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In this paper, we introduce an SU(1, 1) algebraic approach to study the (2 + 1)-Dirac oscillator in the presence of the Aharonov–Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This approach is based on a quantum mechanics factorization method that allows us to obtain the su(1, 1) algebra generators, the energy spectrum and the eigenfunctions. We obtain the coherent states and their temporal evolution for each spinor component of this problem. Finally, for these problems, we calculate some matrix elements and the Schrödinger uncertainty relationship for two general SU(1, 1) operators. [ABSTRACT FROM AUTHOR]

We study the radial part of the Dunkl–Coulomb problem in two dimensions and show that this problem possesses the SU(1,1) symmetry. We introduce two different realizations of the su(1,1) Lie algebra and use the theory of irreducible representations to obtain the energy spectrum and eigenfunctions. For the first algebra realization, we apply the Schrödinger factorization to the radial part of the Dunkl–Coulomb problem to construct the algebra generators. In the second realization, we introduce three operators, one of them proportional to the Hamiltonian of the radial Schrödinger equation. Finally, we use the SU(1,1) Sturmian basis to construct the radial coherent states in a closed form. [ABSTRACT FROM AUTHOR]