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Approximate Energy Spectra of the Quantum Gaussian Well: A Four-parameter Potential Fitting

Mahmoud Farouta,  Ayham Shaera  and  Sameer M. Ikhdaira,b

 a Physics Department, Faculty of Science, An- Najah National University, Nablus, West Bank, Palestine.

b Department of Electrical Engineering, Near East University, Nicosia, Northern Cyprus, Mersin 10, Turkey.

Corresponding Author:  Mahmoud Farout                                         Email: m.qaroot@najah.edu

Doi: https://doi.org/10.47011/15.5.6

Cited by : Jordan J. Phys., 15 (5) (2022) 487-494


Received on: 11/03/2021;                                                Accepted on: 13/06/2021

Abstract: In this work, we present a detailed study of a one-dimensional Schrödinger equation in the presence of quantum Gaussian well interaction. Further, we investigate the approximate solutions by using the harmonic oscillator approximation, variational principle, four-parameter potential fitting and numerical solution using the finite-difference method. The parabolic approximation yields an excellent energy value compared with the numerical solution of the Gaussian system only for the ground state, while for the excited states, it provides a higher approximation. Also, the analytical bound-state energies of the four-parameter potential under the framework of the Nikiforov-Uvarov (NU) method have been used after getting the suitable values of the potential parameters using numerical fitting. The present results of the system states are found to be in high agreement with the well-known numerical results of the Gaussian potential.

Keywords: Gaussian potential, One-dimensional Schrödinger equation, Nikiforov- Uvarov (NU) method, Four-parameter potential.

PACS: 03.65.−w; 02.90.+p; 12.39.Pn.



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