https://doi.org/10.1140/epjp/s13360-022-03534-5
Regular Article
Thin layer quantization method for charged particle on a cone
Laboratory of Theoretical Physics, Department of Physics, University of Jijel, PB 98 Ouled Aissa, 18000, Jijel, Algeria
Received:
9
September
2022
Accepted:
22
November
2022
Published online:
7
December
2022
Using the thin layer method, we describe the dynamics of a charged particle constrained to move on the surface of an infinite straight circular cone and subjected to a static magnetic field. The Gaussian curvature introduces a singular term proportional to two dimensional 
-function in the surface part of the Schrödinger equation. We will regularize the problem by a redefinition of the Gaussian curvature term as a limit of a less singular model. The bound state energies are implicitly determined by a transcendental equation. The well known Landau levels are obtained as limiting case. For the special case 
of the azimuthal quantum number, the Schrödinger equation contains in addition to Dirac delta function a singular inverse square potential in the strong coupling regime. For a time dependent magnetic field, we will employ the Lewis and Riesenfeld invariant theory to show that the problem is exactly solvable. For the case , the problem requires a regularization method. The time independent results are recovered.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
