Calisir, Ayse DoganTuran, MehmetTuran, MehmetAdiguzel, Rezan SevinikSevinik Adıgüzel, RezanMathematics2024-07-052024-07-05202300170-42141099-147610.1002/mma.95862-s2.0-85166530335https://doi.org/10.1002/mma.9586https://hdl.handle.net/20.500.14411/2199In this work, the q-deformed Schr & ouml;dinger equations defined in different form of the q-Hamiltonian for q-harmonic oscillator are considered with symmetric, asymmetric, and non-polynomial potentials. The spectrum of the q-Hamiltonian is obtained by using the Rayleigh-Ritz variational method in which the discrete q-Hermite I polynomials are taken as the basis. As applications, q-harmonic, purely q-quartic, and q-quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the q-version of Gaussian potential for an example of a non-polynomial symmetric potential and a specific example of q-version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of q. The limit relation as q ? 1(-) is discussed. The obtained results of ground-and excited-state energies of the purely q-quartic oscillator and the accuracy of the ground-state energy levels are compared with the existing results. Also, the results are compared with the classical case appearing in the literature in the limiting case q?1(-).eninfo:eu-repo/semantics/closedAccessdiscrete Schr & oumldinger equationdiscrete q-Hermite I polynomialspurely q-quartic oscillatorRayleigh-Ritz variational methodArticleQ146181869318705WOS:001040693600001