SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states

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Abstract

© 2017, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg. We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.
Original languageAmerican English
JournalEuropean Physical Journal Plus
DOIs
StatePublished - 1 Jan 2017

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Algebra
algebra
oscillators
Hamiltonians
Factorization
factorization
energy spectra
generators

Cite this

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title = "SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states",
abstract = "{\circledC} 2017, Societ{\`a} Italiana di Fisica and Springer-Verlag Berlin Heidelberg. We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schr{\"o}dinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schr{\"o}dinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.",
author = "M. Salazar-Ram{\'i}rez and D. Ojeda-Guill{\'e}n and Mota, {R. D.} and Granados, {V. D.}",
year = "2017",
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language = "American English",
journal = "European Physical Journal Plus",
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T1 - SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states

AU - Salazar-Ramírez, M.

AU - Ojeda-Guillén, D.

AU - Mota, R. D.

AU - Granados, V. D.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - © 2017, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg. We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.

AB - © 2017, Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg. We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.

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