Theoretic quantum information entropies for the generalized hyperbolic potential

The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov-Uvarov-Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low-lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki-Birula and Mycielski and the Stam-Cramer-Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered.     

Enhancement of the photocatalytic activity of TiO(2) by doping it with calcium ions

Titanium dioxide (TiO(2)) with an enhanced photocatalytic activity was developed by doping it with calcium ions through a sol-gel method. The developed photocatalysts were characterized by Fourier transform infrared (FTIR) spectroscopy, N(2) physisorption, X-ray photoelectron spectroscopy (XPS), and X-ray diffraction. Their surface morphologies were studied using surface scanning electron microscopy (SEM). The XPS analyses confirmed the presence of Ti, O, Ca, and C in the Ca-doped TiO(2) sample. The activities of the catalysts were evaluated by photocatalytic degradation of an azo dye, acid red 1 (AR1), using UV light irradiation. The results of the investigations revealed that the samples calcined at 300 °C for 3.6h in a cyclic (2 cycles) mode had the best performance. Lower percentage dopant, 0.3-1.0 wt.%, enhanced the photocatalytic activity of TiO(2), with the best at 0.5 wt.% Ca-TiO(2). The performance of 0.5 wt.% Ca-TiO(2) in the degradation of AR1 was far superior to that of a commercial anatase TiO(2) Sigma product CAS No. 1317-70-0. The effect of pH on the degradation of AR1 was studied, and the pH of the dye solution exerted a great influence on the degradation of the dye.     

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.     

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r,θ)=V(r)+(?²/2Mr²) [(βsin²θ +γcos²θ +λ)/sin θcosθ]² and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ)=(?²/2Mr²) [(βsin²θ +γcos²θ +λ)/sin θcosθ]², which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.     

Relativistic symmetries of Deng Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interactions

Relativistic symmetries of the Dirac equation under spin and pseudo-spin symmetries are investigated and a combina- tion of Deng-Fan and Eckart potentials with Coulomb-like and Yukawa-like tensor interaction terms are considered. The energy equation is obtained by using the Nikiforov-Uvarov method and the corresponding wave functions are expressed in terms of the hypergeometric functions. The effects of the Coulomb and Yukawa tensor interactions are numerically discussed as well.     

Solutions of Dirac Equation for Generalized Hyperbolical Potential Including Coulomb-Like Tensor Potential with Spin Symmetry

We solved the Dirac equation for the generalized hyperbolical potential including a Coulomb-like tensor potential under spin symmetry with spin-orbit quantum number k. We used the parametric generalization of the Nikiforov–Uvarov method to obtain the energy eigenvalue and the unnormalized wave function.     

Bound state solutions of d-dimensional Schrdinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrdinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method.We obtain energy eigenvalues and the corresponding wave function expressed in terms of a Jacobi polynomial.We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions.Numerical results are also computed for the energy spectrum and the potentials.     

Analytical Approximate Solution of SchrSdinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary/-State

We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.     

Pseudospin symmetry of the Dirac equation for a Mobius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics.We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner.We comment on the system via various useful figures and tables.     

Approximate solutions of Dirac equation for Tietz and general Manning-Rosen potentials using SUSYQM

In this paper, we consider the relativistic Dirac equation with Tietz and general Manning-Rosen potential. By using appropriate approximation, we obtained the approximate analytical solutions of the Dirac equation for the combined potential via the supersymmetric quantum mechanics (SUSYQM). Within the framework of spin and pseudospin symmetry limits, we obtained the relativistic energy eigenvalus and the corresponding components of the wave functions for Tietz and Manning-Rosen potential using the SUSYQM. We have also reported some numerical results and figures to show the effect of the tensor interactions.