On Behavior of Quantum Particles in an Electric Field in Spaces of Constant Curvature, Hyperbolic and Spherical Models
Keywords:Electric field, spaces of constant curvature, Schr¨odinger equation, Dirac equation, exact solutions
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.
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