# 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:

- Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus)
- (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. Mon .
"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 = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4960474

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