Turan, MehmetAdiguzel, Rezan SevinikCalisir, Ayse DoganMathematics2024-07-052024-07-0520210217-751X1793-656X10.1142/S0217751X215002022-s2.0-85100597979https://doi.org/10.1142/S0217751X21500202https://hdl.handle.net/20.500.14411/1898In this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.eninfo:eu-repo/semantics/closedAccessDiscrete Schrodinger equationq-harmonic oscillatorRayleigh-Ritz variational methoddiscrete q-Hermite I polynomialsArticleQ3Q3363WOS:0006174956000032