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

  • Daniel A. BonillaEmail author
  • Alberto Martín-RuizEmail author
  • Luis F. UrrutiaEmail author
Regular Article


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.

Graphical abstract


Atomic Physics 


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Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de Física, Pontificia Universidad Católica de ChileSantiagoChile
  2. 2.Instituto de Ciencia de Materiales de Madrid, CSICMadridSpain
  3. 3.Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de MéxicoMéxico, Distrito FederalMéxico
  4. 4.Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de MéxicoMéxico, Distrito FederalMéxico

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