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International Journal of Modern Physics A

Dimensionality and screening parameter effects on energy spectra and thermodynamics of exponential pseudo-harmonic oscillator

U. S. Okorie, Haifa I. Alrebdi, Gaotsiwe Joel Rampho, Akpan N. Ikot

Published Jan 16, 2026• 1 citation
Publisher

Abstract

In this study, we employ the extended Nikiforov–Uvarov method to solve the d-dimensional Schrödinger equation with exponential pseudo-harmonic potential. With the help of Greene–Aldrich approximation scheme, analytical expression of the approximate energy eigenvalues and wave function was obtained in closed form and in terms of confluent Heun function, respectively. In addition, expressions of partition function and other thermodynamic functions for the exponential pseudo-harmonic potential were obtained, as they relate with temperature, screening parameter and dimensionality. Numerical and graphical variations of the energies and thermodynamic functions have been presented for various quantum states, temperature, screening parameter and dimensionality values. It is observed that energy eigenvalues and thermodynamic functions of the exponential pseudo-harmonic potential are significantly affected by the screening parameters, dimensionality, temperature and quantum state values considered. Special results for pseudo-harmonic and harmonic potentials are realized as the screening parameter approaches zero. Our results agree with some physical phenomena in condensed matter and atomic physics.

DOI
10.1142/s0217751x2650051x

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In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system’s energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system’s thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields.
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In this study, an approximate solution of the Schrödinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov–Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.