Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators

Abstract

The intertwining technique has been widely used to study the Schrödinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the system to be solved is a relativistic particle placed in a magnetic field with cylindrical symmetry whose intensity decreases as the distance to the symmetry axis grows and its field lines are parallel to the $x-y$ plane. It will be shown that the Hamiltonian under study turns out to be shape invariant.

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Cited by in corpus (6)

• The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
• The effect of tensor interaction in splitting the energy levels of relativistic systems
• The solutions of Dirac equation on the hyperboloid under perpendicular magnetic fields
• Two-dimensional Dirac fermion in presence of an asymmetric vector potential
• Dirac-like Hamiltonians associated to Schrödinger factorizations
• Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators