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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]

By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of d d x . Also, by changing the derivative d d x by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator H SIO = − 1 2 d 2 d x 2 − 1 2 x 2 , we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given. [ABSTRACT FROM AUTHOR]