This article is cited in 24 papers

Solutions of the Dirac equation in a magnetic field and intertwining operators

Alonso Contreras-Astorga^a, David J. Fernández C.^a, Javier Negro<sup>b

a</sup> Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico
^b Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47071 Valladolid, Spain

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.

Keywords: intertwining technique; supersymmetric quantum mechanics; Dirac equation.

MSC: 81Q05; 81Q60; 81Q80

Received: July 31, 2012; in final form October 17, 2012; Published online October 28, 2012

Language: English

DOI: 10.3842/SIGMA.2012.082

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ArXiv: 1210.7416