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Title: Coherent states on horospheric three-dimensional Lobachevsky space

Abstract

In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.

Authors:
;  [1];  [1];  [2];  [2]
  1. Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus)
  2. (Portugal)
Publication Date:
OSTI Identifier:
22596417
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; EIGENSTATES; HAMILTONIANS; LOBACHEVSKY GEOMETRY; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by, Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by, Rybak, I., E-mail: Ivan.Rybak@astro.up.pt, Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto, and Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto. Coherent states on horospheric three-dimensional Lobachevsky space. United States: N. p., 2016. Web. doi:10.1063/1.4960474.
Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by, Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by, Rybak, I., E-mail: Ivan.Rybak@astro.up.pt, Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto, & Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto. Coherent states on horospheric three-dimensional Lobachevsky space. United States. doi:10.1063/1.4960474.
Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by, Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by, Rybak, I., E-mail: Ivan.Rybak@astro.up.pt, Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto, and Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto. 2016. "Coherent states on horospheric three-dimensional Lobachevsky space". United States. doi:10.1063/1.4960474.
@article{osti_22596417,
title = {Coherent states on horospheric three-dimensional Lobachevsky space},
author = {Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by and Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by and Rybak, I., E-mail: Ivan.Rybak@astro.up.pt and Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto and Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto},
abstractNote = {In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.},
doi = {10.1063/1.4960474},
journal = {Journal of Mathematical Physics},
number = 8,
volume = 57,
place = {United States},
year = 2016,
month = 8
}