Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory

  • Yu. A. Kurochkin B.I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Keywords: Lobachevskii space, horosphere, Fourier transform, coordinates, Schr¨odinger equation, scattering, amplitude of scattering, analytical representation, method, iterations, finite differences

Abstract

The problem of the motion of a free particle in the three-dimensional Lobachevskii space are interpreted as scattering by the space. The quantum-mechanical case is considered on the basis of the integral equation derived from the Schr¨odinger equation. After the separation of variables in a quasi-Cartesian coordinate system, the integral equation is derived for the momentum component along the axis of symmetry of a horosphere, which coincides with the z axis. The relationship between the scattering amplitude and analytical functions is established. The methods of iteration and finite differences are used to solve the integral equation.

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Published
2019-12-09
How to Cite
Kurochkin, Y. (2019). Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory. Ukrainian Journal of Physics, 64(12), 1108. https://doi.org/10.15407/ujpe64.12.1108
Section
Fields and elementary particles