Statistical analysis and information theory of screened Kratzer–Hellmann potential model

Abstract

In this research, the radial Schrodinger equation for a newly proposed screened Kratzer-Hellmann potential model was studied via the conventional Nikiforov-Uvarov method. The approximate bound state solution of the Schrodinger equation was obtained using the Greene-Aldrich approximation in addition to the normalized eigenfunction for the new potential model, both analytically and numerically. These results were employed to evaluate the rotational-vibrational partition function and other thermodynamic properties for the screened Kratzer-Hellmann potential. The results obtained have been graphically discussed. Also, the normalized eigenfunction has been used to calculate some information-theoretic measures including Shannon entropy and Fisher information for low lying states in both position and momentum spaces numerically. The Shannon entropy results obtained agreed with the Bialynicki-Birula and Mycielski inequality, while the Fisher information results obtained agreed with the Stam, Crammer-Rao inequality. Also, an alternating increasing and decreasing localization across the screening parameter for both eigenstates were observed.

Analyzing the effects of magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules

“…The partition function of VSCP is obtained by calculating Equation () with the maple software, and the resulting equation is expressed as: where Osobonye et al [61] express the imaginary error function as …”

Entropic uncertainty relations and the fisher information for the Generalized radial Yukawa potential

“…However, the study of information theory of quantummechanical systems have been extensively used in recent years to study a variety of quantum mechanical systems (Majernik, et al, 1996;Yanez, et al, 1994;Dehesa, et al, 1997;Dehesa, et al, 2006;Yahya, et al, 2014a;Yahya, et al, 2014b;Yahya, et al, 2013;Osobonye, et al, 2020;Patil, et al, 2007;Isonguyo, et al, 2018;Okon, et al, 2018 andAntia, et al, 2018). This is because, it provides a deeper knowledge into the internal structure of the quantum systems and it is closely related with modern quantum computation and information, which is a basic theory for numerous technological developments (Gadre, et al, 1991 andNielson, 2001).…”

Approximate analytical solutions of the Schrodinger equation in central potential field

“…A combination of two potentials has aroused extensive research interest in literature. Many researchers have adopted this type of potential to carry out some works [8,9,10,11,12,13,14,15]. Motivated by these works, we consider the following form of potential model which is the superposition of Hulthn [16] and a class of Yukawa [17] potentials…”