The Bohr Hamiltonian with four inverse power terms potential for the [Formula: see text]-part and a harmonic oscillator for the [Formula: see text]-part is solved. The [Formula: see text]-part has been solved using the biconfluent Heun equation. The total wave function and energy have been derived. The numerical results for energy triaxial nuclei spectra are compared with the experimental data, esM and esKM models known for [Formula: see text] atomic nuclei. These results are in overall good agreement with the experimental data. After this, the corresponding [Formula: see text] transition rates have been calculated for each nuclei of Platinum.
In this paper, we determine eigen energies, eigenfunctions and statistical properties of non-relativistic heavy quarkonia interacting with the extended Cornel potential within a space-time generated by a cosmic-string. We extend the Cornel potential by adding the inverse square potential plus the quadratic potential. We have calculated the energy eigenvalues and the corresponding eigenstates using the Extended Nikiforov-Uvarov (ENU) method. Then, based on the equation of energy spectra, the thermodynamic properties like partition function, entropy, free energy, mean energy and specific heat capacity are calculated within the space-time of a cosmic-string. In the next step, we investigate the influence of the cosmic-string parameter on quantum states of heavy quarkonia and their statistical properties.
A novel technique is presented to analytically solve the fractional diffusion equation for non-reactive air pollutants emitted from an elevated continuous source into the air. A generalized methodical solution combining first-order Wentzel–Kramers–Brillouin (WKB) approximation theory and the Sturm–Liouville problem is used to solve the air pollutants’ fractional dispersion equation. Drawing insight from previous analysis, we expanded the initial issue assuming the turbulent flow characteristics appearing in the diffusion process in a non-integer dimensional space. We solved the transformed problem and compared the solutions against data from real experiment. Physical consequences connecting to the conventional generalized diffusion equations are presented. The results indicate that the present solutions are in accordance with those obtained in literature. This report demonstrates that fractional equations can be applied in a practical prediction of pollutant dissemination in a turbulent atmosphere.
In this paper, we study the Schrödinger equation with non-central modified Killingbeck potential plus a ring-shaped-like potential problem, which is not spherically symmetric. The factorization method is used to solve the hypergeometric equation types which lead to solutions with the associate Laguerre function for the radial part and Jacobi polynomial for the polar part. We introduce the raising and lowering operators to calculate the energies eigenvalues, which show that the lack of spherical symmetry removes the degeneracy of second quantum number m which is completely expected. These obtained energies are better to explain the superposition of the energy levels of the atoms in the crystalline structure of molecules.
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