Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

The behavior of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, wherein two one-dimensional Schrodinger Hamiltonians are intertwined by a first-order differential operator. Special magnetic fields are initially chosen, in order that will be shape-invariant, exactly solvable potentials. When looking for more general first-order operators intertwining H- with a not-necessarily shape-invariant Hamiltonian, new magnetic fields associated also with analytic solutions will be generated. The iteration of this procedure is also discussed.