Exact solution of the Schrödinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
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Date
2019
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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 Schr¨odinger 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.