Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 082, 10 pages      arXiv:1210.7416      https://doi.org/10.3842/SIGMA.2012.082
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

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

Alonso Contreras-Astorga a, David J. Fernández C. a and Javier Negro b
a) 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

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

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.

Key words: intertwining technique; supersymmetric quantum mechanics; Dirac equation.

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