Spectrum of a q-deformed Schrödinger equation by means of the variational method


Doğan Çalışır A., Turan M., Sevinik Adıgüzel R.

Mathematical Methods in the Applied Sciences, vol.46, no.18, pp.18693-18705, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 18
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.9586
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.18693-18705
  • Keywords: discrete q-Hermite I polynomials, discrete Schrödinger equation, purely q-quartic oscillator, Rayleigh-Ritz variational method
  • Middle East Technical University Affiliated: No

Abstract

In this work, the (Formula presented.) -deformed Schrödinger equations defined in different form of the (Formula presented.) -Hamiltonian for (Formula presented.) -harmonic oscillator are considered with symmetric, asymmetric, and non-polynomial potentials. The spectrum of the (Formula presented.) -Hamiltonian is obtained by using the Rayleigh-Ritz variational method in which the discrete (Formula presented.) -Hermite I polynomials are taken as the basis. As applications, (Formula presented.) -harmonic, purely (Formula presented.) -quartic, and (Formula presented.) -quartic oscillators are examined in the class of symmetric polynomial potentials. Moreover, the (Formula presented.) -version of Gaussian potential for an example of a non-polynomial symmetric potential and a specific example of (Formula presented.) -version of asymmetric double well potential are presented. Numerous results are given for these potentials for several values of (Formula presented.). The limit relation as (Formula presented.) is discussed. The obtained results of ground- and excited-state energies of the purely (Formula presented.) -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 (Formula presented.).