Regular Article

Exact solution of the Schrödinger equation for a hydrogen atom at the interface between the vacuum and a topologically insulating surface

¹ Facultad de Física, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile
² Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049 Madrid, Spain
³ Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 México, Distrito Federal, México
⁴ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 México, Distrito Federal, México

^a e-mail: dabonilla@uc.cl
^b e-mail: alberto.martin@nucleares.unam.mx
^c e-mail: urrutia@nucleares.unam.mx

Received: 12 July 2018
Received in final form: 24 January 2019
Published online: 1 June 2019

Abstract

When a hydrogen atom is brought near the interface between θ-media, the quantum-mechanical motion of the electron will be affected by the electromagnetic interaction between the atomic charges and the θ-interface, which is described by an axionic extension of Maxwell electrodynamics in the presence of a boundary. In this paper we investigate the atom-surface interaction effects upon the energy levels and wave functions of a hydrogen atom placed at the interface between a θ-medium and the vacuum. In the approximation considered, the Schrödinger equation can be exactly solved by separation of variables in terms of hypergeometic functions for the angular part and hydrogenic functions for the radial part. In order to make such effects apparent we deal with unrealistic high values of the θ-parameter. We also compute the energy shifts using perturbation theory for a particular small value of θ and we demonstrate that they are in very good agreement with the ones obtained from the exact solution.