Spectrum of a q-deformed Schrödinger equation by means of the variational method
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
In 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(-).
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Keywords
discrete Schr & ouml, dinger equation, discrete q-Hermite I polynomials, purely q-quartic oscillator, Rayleigh-Ritz variational method
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0
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Q1
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Source
Volume
46
Issue
18
Start Page
18693
End Page
18705