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
- 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/).
Cite this article
TY - JOUR AU - D. Ojeda-Guillén AU - M. Salazar-Ramírez AU - R. D. Mota AU - V. D. Granados PY - 2021 DA - 2021/01/06 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 - 10.1080/14029251.2016.1248158 ID - Ojeda-Guillén2021 ER -