Abstract
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 Schrödinger 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.
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