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

Abstract

When an hydrogen atom is brought near to the interface between $\theta$-media, the quantum-mechanical motion of the electron will be affected by the electromagnetic interaction between the atomic charges and the $\theta$-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 an hydrogen atom placed at the interface between a $\theta$-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 $\theta$-parameter. We also compute the energy shifts using perturbation theory for a particular small value of $\theta$ and we demonstrate that they are in a very good agreement with the ones obtained from the exact solution.

arXiv comment20 pages, 17 figures, 6 tables, Accepted for publication in the European Physics Journal D

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Cited by in corpus (3)

• Optical response of a topological-insulator--quantum-dot hybrid interacting with a probe electric field
• Optical intersubband properties of a core-shell semiconductor-topological insulator quantum dot described by $\theta$-Electrodynamics
• Ground state and polarization of an hydrogen-like atom near a Weyl semimetal