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

Doğan Çalışır, Ayşe
Turan, Mehmet
Sevinik Adıgüzel, Rezan
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Mathematical Methods in the Applied Sciences
In this work, the q-deformed Schrödinger equations defined in different form of the q - Hamil tonian for q-harmonic oscillator studied in [5] 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 dou ble 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 −.
Published by Mathematical Methods in the Applied Sciences; https://doi.org/10.1002/mma.9586; Ayşe Doğan Çalışır, Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey; Mehmet Turan, Rezan Sevinik Adıgüzel, Department of Mathematics, Atilim University, 06830, Ankara, Turkey.
Discrete Schrödinger equation; purely q-quartic oscillator; Rayleigh-Ritz variational method; discrete q-Hermite I polynomials.