Narrow Results

Dirac equation is solved for Mie-type potential. The energy spectra and the corresponding wave functions are investigated with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used to obtain an analytical solution of the Dirac equation and closed forms of energy eigenvalues are obtained for any spin-orbit coupling term κ. We also present some numerical results of Dirac particles for the well-known Kratzer–Fues and modified Kratzer potentials which are Mie-type potential.

In this paper, we solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

In this paper, we investigate the approximate analytical solutions of the relativistic Duffin–Kemmer–Petiau equation in the presence of a Mie-Type potential in noncommutative space by using the Nikiforov–Uvarov method. We determine the energy eigenvalues and eigenfunctions of the DKP equation. Furthermore, energy shift due to noncommutativity space–time is obtained via the perturbation theory. We observe that this feature is comparable to the Zeeman effect and the degeneracy of the classical spectral line is fractured in the transition from commutative to noncommutative space by the splitting of the states.

We investigate the effect of Mie-type potential range on the cohesive energy of metallic nanoparticles using the size-dependent potential parameters method. The predicted cohesive energy for different cubic structures is observed to decrease with decreasing the particle size, and increase with decreasing the range of the interatomic potential, a result which is in the right direction at least to predict the experimental values of Molybdenum and Tungsten nanoparticles.