Abstract
We present a new approach to study a class of non-Hermitian ([Formula: see text])-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well-known Nikiforov–Uvarov method to solve such a system. We discuss applications and explore the solvability of both [Formula: see text]-symmetric and non[Formula: see text]-symmetric classes of potentials. In the former case, we obtain the solution of a harmonic oscillator in the presence of a linear vector potential while in the latter case we solve the shifted harmonic oscillator problem.
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