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

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.