Related papers: Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space

Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space

URL: http://arxiv.org/abs/2305.11879v1
Date: Sun, 7 May 2023 17:03:00 GMT
Title: Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space
Authors: Alexander J. Silenko
Abstract summary: Graphene electrons in a static electric field can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. It is proven that the Hermite-Gauss beams exist even in the free space.
Score: 91.3755431537592
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The relativistic Foldy-Wouthuysen transformation is used for an advanced description of planar graphene electrons in external fields and free (2+1)-space. It is shown that the initial Dirac equation should contain usual Dirac matrices but not the Pauli ones. The spin of graphene electrons is not the isotopic spin and takes the values $\pm1/2$. The exact Foldy-Wouthuysen Hamiltonian of a graphene electron in uniform and nonuniform magnetic fields is derived. The exact energy spectrum agreeing with experimental data and exact Foldy-Wouthuysen wave eigenfunctions are obtained. These eigenfunctions describe multiwave (structured) states in (2+1)-space. It is proven that the Hermite-Gauss beams exist even in the free space. In the multiwave Hermite-Gauss states, graphene electrons acquire nonzero effective masses dependent on a quantum number and move with group velocities which are less than the Fermi velocity. Graphene electrons in a static electric field also can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. These beams can be accelerated and decelerated.

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