The energy spectrum of a new exponentially confining potential
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The energy spectrum of a new exponentially confining potential Ibsal Assi1,a , Abdullah Sous2 , Hocine Bahlouli3 1 Department of Physics and Physical Oceanography, Memorial University of Newfoundland,
St. John’s, NL A1B 3X7, Canada
2 Faculty of Technology and Applied Sciences, Al-Quds Open University, Nablus, Palestine 3 Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Received: 9 September 2020 / Accepted: 18 November 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we consider a general Morse-type confining potential that was introduced recently by Alhaidari (J Theor Math Phys 205, 2020. arXiv:2005.09080). This potential is completely confining and hence has an infinite discrete spectrum. We compute the energy spectrum associated with this confining potential using two different approaches so as to ensure the correctness of our results. We use both asymptotic iteration method and the numerical diagonalization method based on the tridiagonal representation approach of our unperturbed Hamiltonian to compute the energy spectrum. We found that both approaches resulted in bound state energies that are in agreement with each other to a high degree of accuracy.
1 Introduction Physically bound states are solutions which are localized in space, as opposed to plane wave solutions which are extended or delocalized in space. Mathematically, they represent simply the allowed energy levels for the system which can be represented by square integrable solutions of the associated Schrodinger equation. These states are confined in space and typically decay exponentially asymptotically. Potentials that give rise to such bound states and hence confine electrons can possess various shapes depending on the nature of the system and its boundary conditions. The structure of the bound state spectrum depends heavily on the profile and asymptotic behavior of the confining potential. Thus, knowledge of the realistic profile of the confining potential is important in theoretical investigations of the electronic properties of bound states. Among the most famous traditional confining potentials are the rectangular potential well [1,2] and the parabolic or harmonic oscillator potential trap [3]. Experimentally bounds states can be probed using a variety of techniques ranging from scanning and tunneling microscopy to various scattering experiments. In fact, modern electronic devices like quantum well lasers, resonant tunneling diodes, sensors and detectors rely heavily on the spatial and energetic position of such bound states which play
Electronic supplementary material The online version of this article (https://doi.org/10.1140/epjp/ s13360-020-00955-y) contains supplementary material, which is available to authorized users. a e-mail: [email protected] (corresponding author)
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a major role in defining the transport and optical properties of thes
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