Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields

Abstract

Two dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parametrization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with the position dependent mass Hamiltonians. We introduce two ansatzes for the component of the vector potential to acquire effective solvable models, which are Rosen Morse II potential and the model given in [52] whose bound states are Jacobi X 1 type polynomials, and we adapt our work to these special models under some parameter restrictions. The energy spectrum and the eigenvectors are found for Rosen Morse II potential. On the other hand, complete solutions are given for the second system. The vector and the effective potentials with their eigenvalues are sketched for each system.

Supersymmetric quantum electronic states in graphene under uniaxial strain

“…In particular, it is well known that the Dirac equation in some electromagnetic potentials can be factorized according to a supersymmetric structure in the quantum mechanical sense [5,6,7]. This fact has been exploited to study several properties of graphene [8,9,10,11,12,13,14] and other Dirac-like materials [15,16,17] connected with the influence of external magnetic fields, as well as charge impurities which induce the atomic collapse effect when a supercritical regime is reached at [18]. Interestingly, considering a non-uniform magnetic field perpendicularly aligned to a membrane of graphene, in Ref.…”

Dirac equation in the curved spacetime and generalized uncertainty principle: A fundamental quantum mechanical approach with energy-dependent potentials

“…where a, c are constants. Hence, we can find U 1 (r) and other related energy dependent potentials V (r) and S(r) using (10), (11), (17) and (18):…”

“…The Dirac equation in low dimensions (2 + 1) has been intensely studied for the past three decades by many authors in theoretical physics [9], [10], [11], [12]. The low dimensional systems have always been attracting attention due to theoretical and experimental interesting results such as high energy particle theory, condensed matter physics (monolayer structures), topological field theory, and string theory.…”