Journal of Nonlinear Mathematical Physics

Volume 23, Issue 4, September 2016, Pages 607 - 619

SU(1, 1) and SU(2) Perelomov number coherent states: algebraic approach for general systems

Authors
D. Ojeda-Guillén
Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Del. Gustavo A. Madero, C.P. 07738, México D. F., Mexico, dojedag@ipn.mx
M. Salazar-Ramírez
Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Del. Gustavo A. Madero, C.P. 07738, México D. F., Mexico, escomphysics@gmail.com
R. D. Mota
Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D. F., Mexico, rdmotae@yahoo.com.mx
V. D. Granados
Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738 México D. F., Mexico, granados@esfm.ipn.mx
Received 5 April 2016, Accepted 14 September 2016, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1248158How to use a DOI?
Keywords
coherent states, Lie algebras, pseudoharmonic oscillator, two-dimensional harmonic oscillator
Abstract

We study some properties of the SU(1, 1) Perelomov number coherent states. The Schrödinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number coherent states. It is shown that this relationship is minimized for the standard coherent states. We obtain the time evolution of the number coherent states by supposing that the Hamiltonian is proportional to the third generator K0 of the su(1, 1) Lie algebra. Analogous results for the SU(2) Perelomov number coherent states are found. As examples, we compute the Perelomov coherent states for the pseudoharmonic oscillator and the two-dimensional isotropic harmonic oscillator.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 4
Pages
607 - 619
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1248158How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - D. Ojeda-Guillén
AU  - M. Salazar-Ramírez
AU  - R. D. Mota
AU  - V. D. Granados
PY  - 2021
DA  - 2021/01
TI  - SU(1, 1) and SU(2) Perelomov number coherent states: algebraic approach for general systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 607
EP  - 619
VL  - 23
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1248158
DO  - https://doi.org/10.1080/14029251.2016.1248158
ID  - Ojeda-Guillén2021
ER  -