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arXiv:2212.13601 · Boletín de la Sociedad Matemática Mexicana

q-Deformed coherent states associated with the sequence $$x_n^{q,\alpha }=(1+\alpha q^{n-1})[n]_q$$

Othmane El Moize, Zouhaı̈r Mouayn, Khalid Ahbli

Published Jul 24, 2024• 0 citations
arXivHTMLPDF
DOI
10.1007/s40590-024-00649-w

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q-Deformed coherent states associated with the sequence xnq,α=(1+αqn−1)[n]qx_n^{q,\alpha }=(1+\alpha q^{n-1})[n]_qxnq,α​=(1+αqn−1)[n]q​
In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.