One-dimensional Coulomb problem in Dirac materials
Downing, C.A.; Portnoi, M.E.
Date: 20 November 2014
Article
Journal
Physical Review A - Atomic, Molecular, and Optical Physics
Publisher
American Physical Society
Publisher DOI
Abstract
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wave functions expressed in terms of special functions (namely, Whittaker ...
We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wave functions expressed in terms of special functions (namely, Whittaker functions), while the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical band gaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.
Physics and Astronomy
Faculty of Environment, Science and Economy
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