In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein–Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n = 0, 1, 2 are calculated. Some interesting features of both Fisher and Shannon densities, as well as the probability densities, are demonstrated. Finally, the Stam, Cramer–Rao and Bialynicki–Birula–Mycielski (BBM) inequalities have been checked, and their comparison with the regarding results have been reported. We showed that the BBM inequality is still valid in the form [Formula: see text], as well as in ordinary quantum mechanics.

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On the basis of ab initio calculations employing density functional theory (DFT), we investigate the structural, electronic, optical and thermodynamic properties of two binaries: PbS and PbSe in rock-salt structures. In addition, several compositions with various ordered structures of PbS 1-x Se x alloys were studied. The calculations were performed using the full potential linearized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA). Various quantities, such as equilibrium lattice constants, bulk modulus, band structures and refractive index for all Se -concentrations are presented. The microscopic origins of the gap bowing were explained by using the approach of Zunger and coworkers. On the other hand, the thermodynamic stability of these alloys was investigated by calculating the excess enthalpy of mixing ΔHm as well as the phase diagram.

The structural, electronic, optical and thermodynamic properties of Mg1−xSrxO ternary alloys in NaCl structures at various Sr concentrations are presented. The calculations were performed using the full potential linearized augmented plane wave (FP-LAPW) method within the density functional theory (DFT) in the local density approximation (LDA) and two developed refinements, namely the generalized gradient approximation (GGA) of Perdew et al (1996 Phys. Rev. Lett. 77 3865) for the structural properties and Engel and Vosko (1993 Phys. Rev. B 47 13164) for the band structure calculations. Deviation of the lattice constants from Vegard's law and the bulk modulus from the linear concentration dependence (LCD) were observed for the alloys. The microscopic origins of the gap bowing were explained by using the approach of Bernard and Zunger (1986 Phys. Rev. Lett. 34 5982). The refractive index and optical dielectric constant for the alloys of interest were calculated by using different models. In addition, the thermodynamic stability of the alloys was investigated by calculating the critical temperatures of alloys.

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