Álvarez Nodarse, RenatoAtakishiyeva Kyazim Zade, MessoumaAtakishiyev Mektiyev, Natig2016-05-312016-05-312005-11Álvarez Nodarse, R., Atakishiyeva Kyazim Zade, M. y Atakishiyev Mektiyev, N. (2005). On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R. Czechoslovak Journal of Physics, 55 (11), 1315-1320.0011-46261572-9486http://hdl.handle.net/11441/41715We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics, based on a q-extension of the classical Hermite polynomials Hn(x), recently introduced by us in [1] R. Alvarez-Nodarse, M. K. Atakishiyeva, and N. M. Atakishiyev.. On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R. Boletín de la Sociedad Matemática Mexicana (3), 8, No.2, pp.127–139, 2002. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line R with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s10582-006-0003-z