Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory

¹ Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa - 84030-900 Ponta Grossa, PR, Brazil
² Departamento de Física, Universidade Federal do Maranhão - 65085-580 São Luís, MA, Brazil
³ Departamento de Física, Universidade Federal de Lavras - Caixa Postal 3037, 37200-000, Lavras, MG, Brazil
⁴ Departamento de Física, Universidade Federal da Paraíba - Caixa Postal 5008, 58051-900, João Pessoa, Paraíba, Brazil

Received: 3 August 2019
Accepted: 9 October 2019

Abstract

In this work, we study the scattering of a spinless charged particle constrained to move on a curved surface in the presence of the Aharonov-Bohm potential. We begin with the equations of motion for the surface and transverse dynamics previously obtained in the literature (Ferrari G. and Cuoghi G., Phys. Rev. Lett., 100 (2008) 230403) and describe the surface with non-trivial curvature in terms of linear defects such as dislocations and disclinations. Expressions for the modified phase shift, S-matrix and scattering amplitude are determined by applying a suitable boundary condition at the origin, which comes from the self-adjoint extension theory. We also discuss the presence of a bound state obtained from the pole of the S-matrix. Finally, we claim that the bound state, the additional scattering and the dependence of the scattering amplitude with energy are solely due to the curvature effects.