Study of a class of solvable systems and related topics in quantum mechanics

Abstract

We presented a new newlineapproach to study a class of non-Hermitian one-dimensional Dirac Hamiltonian in newlinethe presence of local Fermi velocity. We applied the well-known Nikiforov-Uvarov newlinetechnique to solve such a system and illustrated our results through meaningful newlineapplications. newlineInsights into the electronic structure of graphene substrates have come from theoretical research on the dynamics of Dirac particles in curved spacetime. A particularly effective method for describing the motion of low-energy charge carriers in newlinegraphene is the latter formulation. We studied the Dirac equation in curved space, newlinefor the charge carriers, in the presence of a local Fermi velocity. An explicit parameterization of the spacetime metric for a nanoscroll cylindrical geometry has been newlineprovided. After redefining the wavefunction, we derived two uncoupled equations newlinefor the two components of the wavefunctions. Using a particular choice of Fermi newlinevelocity and magnetic field, we solved the whole equation and plotted the density newlineprofile.