$SU(1,1)$ and $SU(2)$ Perelomov number coherent states: algebraic approach for general systems
Mathematical Physics
2016-11-01 v4 High Energy Physics - Theory
math.MP
Abstract
We study some properties of the Perelomov number coherent states. The Schr\"odinger'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 of the Lie algebra. Analogous results for the 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.
Keywords
Cite
@article{arxiv.1206.1555,
title = {$SU(1,1)$ and $SU(2)$ Perelomov number coherent states: algebraic approach for general systems},
author = {D. Ojeda-Guillén and M. Salazar-Ramirez and R. D. Mota and V. D. Granados},
journal= {arXiv preprint arXiv:1206.1555},
year = {2016}
}