New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium

Varró, Sándor (2013) New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium. LASER PHYSICS LETTERS, 10 (9). ISSN 1612-2011

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Abstract

Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm < 1. The found solutions are expressed in terms of new complex trigonometric polynomials, which form a doubly infinite set labeled by two integer quantum numbers. These quantum numbers represent quantized spectra of the energy-momentum components of the charged particle along the polarization vector and along the propagation direction of the applied electromagnetic plane wave field (which is considered as a laser field of arbitrary high intensity propagating in an underdense plasma). The found solutions may serve as a basis for the description of possible quantum features of mechanisms of acceleration of electrons by high-intensity laser fields.

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