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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 11, p.1065-1072
doi:10.15407/ujpe58.11.1065    Paper

Ovsiyuk E.M., Veko O.V.

I.P. Shamyakin Mozyr State Pedagogical University
(28, Studencheskaya Str., Mozyr 247760, Gomel region, Belarus; e-mail: e.ovsiyuk@mail.ru)

On Behavior of Quantum Particles in an Electric Field in Spaces of Constant Curvature, Hyperbolic and Spherical Models

Section: International Conference “Quantum Groups and Quantum Integrable Systems” Kyiv, June 18–21, 2013
Original Author's Text: English

Abstract: In the Lobachevsky hyperbolic and Riemann spherical spaces, generalized potentials describing a uniform electric field are introduced as solutions of the covariant Maxwell equations. Exact solutions of the Schr?odinger equation in the presence of the electric field are constructed in both models. The similarity of the energy spectra of the particle against the background of a spherical space with the electric field and in the Coulomb field is noted.

Key words: electric field, spaces of constant curvature, Schr?odinger equation, Dirac equation, exact solutions.