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Title: On some integrable systems in the extended lobachevsky space

Abstract

Some classical and quantum-mechanical problems previously studied in Lobachevsky space are generalized to the extended Lobachevsky space (unification of the real, imaginary Lobachevsky spaces and absolute). Solutions of the Schroedinger equation with Coulomb potential in two coordinate systems of the imaginary Lobachevsky space are considered. The problem of motion of a charged particle in the homogeneous magnetic field in the imaginary Lobachevsky space is treated both classically and quantum mechanically. In the classical case, Hamilton-Jacoby equation is solved by separation of variables, and constraints for integrals of motion are derived. In the quantum case, solutions of Klein-Fock-Gordon equation are found.

Authors:
; ;  [1]
  1. National Academy of Sciences of Belarus, Institute of Physics (Belarus)
Publication Date:
OSTI Identifier:
22043897
Resource Type:
Journal Article
Journal Name:
Physics of Atomic Nuclei
Additional Journal Information:
Journal Volume: 74; Journal Issue: 6; Other Information: Copyright (c) 2011 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-7788
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGED PARTICLES; COORDINATES; COULOMB FIELD; INTEGRAL CALCULUS; INTEGRALS; KLEIN-GORDON EQUATION; LOBACHEVSKY GEOMETRY; MAGNETIC FIELDS; MATHEMATICAL SOLUTIONS; QUANTUM MECHANICS; SCHROEDINGER EQUATION

Citation Formats

Kurochkin, Yu. A., E-mail: y.kurochkin@ifanbel.bas-net.by, Otchik, V S, Ovsiyuk, E M, and Shoukavy, Dz V. On some integrable systems in the extended lobachevsky space. United States: N. p., 2011. Web. doi:10.1134/S1063778811060202.
Kurochkin, Yu. A., E-mail: y.kurochkin@ifanbel.bas-net.by, Otchik, V S, Ovsiyuk, E M, & Shoukavy, Dz V. On some integrable systems in the extended lobachevsky space. United States. https://doi.org/10.1134/S1063778811060202
Kurochkin, Yu. A., E-mail: y.kurochkin@ifanbel.bas-net.by, Otchik, V S, Ovsiyuk, E M, and Shoukavy, Dz V. 2011. "On some integrable systems in the extended lobachevsky space". United States. https://doi.org/10.1134/S1063778811060202.
@article{osti_22043897,
title = {On some integrable systems in the extended lobachevsky space},
author = {Kurochkin, Yu. A., E-mail: y.kurochkin@ifanbel.bas-net.by and Otchik, V S and Ovsiyuk, E M and Shoukavy, Dz V},
abstractNote = {Some classical and quantum-mechanical problems previously studied in Lobachevsky space are generalized to the extended Lobachevsky space (unification of the real, imaginary Lobachevsky spaces and absolute). Solutions of the Schroedinger equation with Coulomb potential in two coordinate systems of the imaginary Lobachevsky space are considered. The problem of motion of a charged particle in the homogeneous magnetic field in the imaginary Lobachevsky space is treated both classically and quantum mechanically. In the classical case, Hamilton-Jacoby equation is solved by separation of variables, and constraints for integrals of motion are derived. In the quantum case, solutions of Klein-Fock-Gordon equation are found.},
doi = {10.1134/S1063778811060202},
url = {https://www.osti.gov/biblio/22043897}, journal = {Physics of Atomic Nuclei},
issn = {1063-7788},
number = 6,
volume = 74,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2011},
month = {Wed Jun 15 00:00:00 EDT 2011}
}