Schrödinger particle in magnetic and electric fields in Lobachevsky and Riemann spaces

Abstract

Schrödinger equation in Lobachevsky and Riemann 4-spaces has been solved in the presence of external magnetic field that is an analog of a uniform magnetic field in the flat space. Generalized Landau levels have been found, modified by the presence of the space curvature. In Lobachevsky4-model the energy spectrum contains discrete and continuous parts, the number of bound states is finite; in Riemann 4-model all energy spectrum is discrete. Generalized Landau levels are determined by three parameters, the magnitude of the magnetic field $B$, the curvature radius $\rho$ and the magnetic quantum number $m$. It has been shown that in presence of an additional external electric field the energy spectrum in the Riemann model can be also obtained analytically.

18 pages

References in corpus (3)

• The Landau problem and noncommutative quantum mechanics
• Noncommutative Quantum Mechanics: The Two-Dimensional Central Field
• Goedel-type Universes and the Landau Problem