Spectrum of theq-Schrödinger equation by means of the variational method based on the discreteq-Hermite I polynomials

Abstract

In this work, the [Formula: see text]-Schrödinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of [Formula: see text], and the limiting case as [Formula: see text] is considered. The Rayleigh–Ritz variational method is adopted to the system. The discrete [Formula: see text]-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: [Formula: see text]-harmonic, purely [Formula: see text]-quartic and [Formula: see text]-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.