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



Lobachevskii space, horosphere, Fourier transform, coordinates, Schr¨odinger equation, scattering, amplitude of scattering, analytical representation, method, iterations, finite differences


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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How to Cite

Kurochkin, Y. A. (2019). Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory. Ukrainian Journal of Physics, 64(12), 1108.



Fields and elementary particles