An algebraic solution of [Formula: see text]-dimensional Dirac equation describing the massless Dirac fermions in the presence of both magnetic field perpendicular to the graphene plane and in-plane homogeneous electric field together with a quadratic confinement potential is investigated. The associated energy eigenvalues are obtained within the framework of unitary transformation scheme. It is shown that the decreasing quadratic confinement potential strength leads to the enhancement of the Landau levels.

Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investigated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Moreover, the Lie algebraic analysis is also performed. keyword: Dirac equation, massless fermion, analytical solutions, Lie algebras PACS: 03.65.Fd, 03.65.Ge, 95.30 Sf

In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy-dependent potentials, and position-dependent mass models are investigated for the Dirac Hamiltonians, and an extension of these three potential models and their solutions is also obtained. The energy spectrum and potential graphs for each case are discussed for the α deficit angle.