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In this paper, we examined the effects of transition metal replacement and ordering in 2D [M.sub.3][C.sub.2][O.sub.2] MXene on the electronic structure and thermal and electrical conductivities using the density functional theory and also Boltzmann's transport theory within the constant relaxation time approximation. We derived the following oxygen-functionalized ordered double-metal MXenes T[i.sub.2]Y[C.sub.2][O.sub.2], [Y.sub.2]Ti[C.sub.2][O.sub.2], S[c.sub.2]Y[C.sub.2][O.sub.2], and [Y.sub.2]Sc[C.sub.2][O.sub.2] through the surface and sub-layer tuning. The results revealed that the ordered MXenes give rise to different electronic structure and transport properties. The electronic thermal conductivities obtained in terms of the relaxation time increase with increase in absolute temperature, while the electrical conductivities decrease with increase in temperature. The respective transport properties of [Y.sub.2]Ti[C.sub.2][O.sub.2] and S[c.sub.2]Y[C.sub.2][O.sub.2] were found to be enhanced due to the increased squared band velocity, density of state, and low Seebeck coefficient compared to T[i.sub.2]Y[C.sub.2][O.sub.2] and [Y.sub.2]Sc[C.sub.2][O.sub.2] MXenes. Generally, the MXene materials investigated in this work were found to possess metallic properties with the existence of energy overlap around the Fermi level. The computed formation energies support chemical stability in all the materials. Key words: MXenes, density functional theory, Boltzmann's theory, thermal conductivity, electrical conductivity, Introduction Two-dimensional (2D) materials have emerged as the cornerstone of device fabrications due to their wide surface area compared to their bulk counterparts. Also, in contrast to bulk materials, 2D [...]

The bound state solutions of the Schrödinger equation (SE) under a deformed hyperbolic potential are used in this paper to investigate the correlation between the information content, such as Shannon entropies and Fisher information, and the variance of a quantum system in both momentum and position spaces. The variance was obtained from the expectation moments in conjugated spaces and used to get the uncertainty products, Fisher information products and Shannon entropic sums for different potential parameters. These information measures were observed to vary with the potential parameters and obey their lowest bound inequalities. An increase in the Fisher information leads to a lower uncertainty and less information while decreases in the Fisher information result in higher uncertainties. We proposed a relationship between the Shannon entropies, Fisher information and the variance where an increase in the Fisher information leads to a lower Shannon entropy or a lower spread of the probability distribution and vice versa. The numerical results obtained with the proposed relations agree with the most utilized method in the literature. This current work simplifies the calculation of the Shannon entropies notably for complex potential functions. [ABSTRACT FROM AUTHOR]

In this paper, we obtained the analytical N-dimensional bound state solutions of exponential-type potential functions using the semi-classical Wentzel-Kramers-Brillouin (WKB) approximation method with an improved approximation to the orbital centrifugal barrier. Furthermore, we derived the partition function with the associated thermodynamic properties. We calculated the expectation values () via the Hellmann-Feynman theorem. Our results for the energy levels are in excellent agreement with the best available results obtained by other methods in the existing literature. The variations of the thermodynamic functions with the temperature parameter ([beta]) agree very well with the other results obtained under different potential energy functions. The expectation values conformed to the ones obtained by another approach in previous work. This work demonstrates the exactness of the leading-order WKB approximation. Key words: Manning-Rosen potential, Eckart potential, Hulthen potential, thermodynamic properties, WKB approximation method. Nous obtenons ici les solutions analytiques a N-dimensions des etats lies de potentiels de type exponentiel, en utilisant la methode de l'approximation semi-classique WKB avec une approximation amelioree pour la barriere centrifuge orbitale. Ensuite, nous derivons la fonction de partition avec ses fonctions thermodynamiques associees. Nous calculons les valeurs moyennes () via le theoreme de Hellmann-Feynman. Nos resultats pour les niveaux d'energie sont en excellent accord avec les meilleurs resultats obtenus d'autres methodes retrouves dans la litterature. Les variations des fonctions thermodynamiques avec le parametre de la temperature ([beta]) sont en tres bon accord avec les autres resultats obtenus pour differentes fonctions d'energie potentielle. Les valeurs moyennes obtenues sont conformes a celles obtenues par d'autres approches dans des travaux anterieurs. Ce travail demontre l'exactitude de l'approximation WKB au premier ordre. [Traduit par la Redaction] Mots-cles : potentiel de Manning-Rosen, potentiel d'Eckart, potentiel de Hulthen, proprietes thermodynamiques, methode de l'approximation WKB., 1. Introduction In quantum mechanics and applied physics, the solutions to the wave equations play an important role in understanding the properties of physical systems. Of these properties, the eigen-solutions [...]

This study solves the radial Schrödinger wave equation (RSWE) with the improved Rosen–Morse (IRM) potential constrained by an electromagnetic field. Energy eigenvalues are derived using the parametric Nikiforov–Uvarov method and Pekeris approximation. The internal partition function, isobaric molar heat capacity formula, and magnetization model are then deduced from the equation governing pure vibrational energy states. These analytical models are applied to several pure substances, specifically Br2 (X 1Σg+), BrF (X 1Σ+), ICl (X 1Σg+), and P2 (X 1Σg+) molecules. Numerical approximations of the energy eigenvalues for these molecules closely match their exact values. The isobaric molar heat capacity expression yields mean percentage absolute deviations of 1.6585%, 0.9162%, 1.2193%, and 0.7232% when compared against experimental data for Br2 (X 1Σg+), BrF (X 1Σ+), ICl (X 1Σg+), and P2 (X 1Σg+), respectively. These results align well with other heat capacity models in existing literature. [ABSTRACT FROM AUTHOR]

The solutions of the Schrὅdinger equation for a molecular Mobius square potential are obtained using two elegant traditional methods. In each case, the energy equation is obtained. The pure vibrational energies for seven different molecules are studied using their respective spectroscopic constants and the obtained energy equation. The present results are compared with the standard results and the results of other potential models. The present study shows that the molecular Mobius square potential produces better results compared to some potential models. [ABSTRACT FROM AUTHOR]