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In this paper, a non-relativistic potential model is used to find the solution of radial Schrodinger wave equation by using Crank Nicolson discretization for heavy quarkonia ( ̅, ̅). After solving the Schrodinger radial wave equation, the mass spectrum and hyperfine splitting of heavy quarkonia are calculated with and without relativistic corrections. The root means square radii and decay constants for S and P states of c ̅ and ̅ mesons by using the realistic and simple harmonic oscillator wave functions. The calculated results of mass, hyperfine splitting, root means square radii and decay constants agreed with experimental and theoretically calculated results in the literature.

First principles calculations are carried out to explore the structural, electronic and optical properties of Pure and Cd-doped BaZrO3, an oxide-based perovskite material. To investigate these properties, Ultra-soft pseudo-potential (USP) is used as incorporated in Cambridge Serial Total Energy Package (CASTEP). In this system, the generalized gradient approximation (GGA) proposed by Perdew-Burke Erzenhoff (PBE) is used for exchange correlation potential. Cadmium (Cd) doping at Ba-site is more favorable as compare to Zr-site because new gamma points occurred which not only affects the electronic structure of the BaZrO3 but also reduces the band gap from 3.127eV to 1.326eV and a transformation from indirect to direct band gap occurred. After doping, Fermi level shifted towards valance band which exhibits the characteristic of p-type semiconductor material. In optical properties, the absorption spectrum, refractive index (2.73), dielectric constants, reflectivity and energy loss function of the doped in comparison with pure material is presented. It has good optical response in UV region. The doping changes the optical behavior of BZO drastically thus making this material more effective for optoelectronic applications.

Generalized Chou-Yang model (GCYM) predicts electromagnetic form factors of several hadrons with varying magnitude of strangeness. By using these form factors, the root mean square (RMS) radii of the hadrons such as (π, p, ϕ, Λ, Σ+, Σ−and Ω−)are computed. It is found that there is consistency among the predicted RMS radii of pion and proton by GCYM (and other models) and experimental results. For all hadrons experimental results are not available. Also we find that results of GCYM and from other models are somewhat inconsistent for hadrons other than pion and proton. Though GCYM and other models do not agree for most of the hadrons but they have one similarity that the computed RMS radii seem decreasing with the increase in the strangeness level, separately for mesons as well as for baryons. The experimental results of hadrons other than pion and proton are needed to check the suitability of GCYM and other models as well as in probing the trend of decreasing radii with increase in strangeness content.

The electronic bandstructure, optical and structural properties of pure and Mg-doped CaTiO3 are calculated by using first-principle calculation which is based on the density functional theory. The effect of Mg-dopant on the properties of CaTiO3 perovskite explored by using ultra soft pseudo-potential (USP) and generalized gradient approximation (GGA). The incorporation of Mg at Ca site affected the electronic band structure of CaTiO3 meaningfully by introducing new gamma point. The incorporation of Mg increases the band gap from 1.84 eV to 1.92 eV. The partial density of states of pure CaTiO3 changed after doping cleared the effect of dopant on pure system. Optical properties of both the systems are examined which reveals that the absorption edge shifting from 2.1 eV to 2.5 eV indicates a blue shift whereas the refractive index also increases from 2 to 2.4 after doping. Thus Mg-doped CaTiO3 not only affect the optical properties of the system but also make it and appealing candidate for optical devices.

The pressure induced theoretical investigations of electronic, optical and elastic constants of cubic zirconia (c-ZrO2) are estimated under the effect of hydrostatic pressure (0–40 GPa) by employing first principles based local density approximation (LDA) functional within the framework of density functional theory (DFT). The optimized structural parameters are in excellent agreement with previous theoretical and experimental values. Our calculated bandgap (3.350 eV) at zero pressure shows excellent consistency with previous listed computational results and very favorable approach to experimentally reported bandgap (4.6 eV) with the increment of pressure. Density of states (DOS) predicts dominant contribution of oxygen electrons of 2p-orbital and zirconium electrons of 4d-orbital in valence and conduction band formation. The estimated values of dielectric constant (5.85) and refractive index (2.42) at zero pressure are in good agreement with existing theoretical data. The optical constants are less sensitive to applied pressure and offer significant stability under high pressure. Pressure based elastic parameters exhibit high mechanical stability, more hardness and stiffness, improved ductility and higher elasticity of c-ZrO2 under high pressure.

Baddeleyite TiO2 is one of the most important phases of titanium dioxide, from technological and industrial point of view. We have carried out theoretical investigation by using plane wave ultrasoft pseudopotential methods based on density functional theory. The Electronic band structure, elastic constants and optical properties as well as, the lattice parameters of baddeleyite TiO2 are calculated by using the optimized crystal structure. The bulk modulus, shear modulus, Young׳s modulus and Poisson ratios for baddeleyite TiO2 are also explored. The Debye temperature of baddeleyite TiO2 is investigated by using calculated mean sound velocity. The anisotropy ratios are computed from elastic constants. Our investigated elastic properties are in contrast with the previous reported results of Ma et al. (2009, Phys. Status Solidi B, 246 (9) 2132) by means of the same DFT method. Electronic properties are presented by considering the computed band structure and densities of states (DOS). Furthermore, the results of electronic properties are consistent with the available reported theoretical results. To explore the optical properties of baddeleyite TiO2, the dielectric functions, refractive index, absorption and energy loss spectrums are presented and analyzed by means of the electronic properties. Also, the considered DFT methods in this work are self-consistent.