arXiv subjects

K. Uzun

Publications and source records attributed to K. Uzun.

2 recordsLinked to original sources

arXiv2018

Bound State Solution of the Klein-Fock-Gordon equation with the Hulthén plus a Ring-Shaped like potential within SUSY quantum mechanics

In this paper, the bound state solution of the modified Klein-Fock-Gordon equation is obtained for the Hulthén plus ring-shaped lake potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any $l\neq0$ angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein-Fock-Gordon equation of the Hulthén plus ring-shaped like potential are obtained by Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary $l$ states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to $n_r$ radial and $l$ orbital quantum numbers.

quant-ph↗

arXiv2017

Bound states of the $D$-dimensional Schr\"{o}dinger equation for the generalized Woods-Saxon potential

In this paper, the approximate analitical solutions of the hyper-radial Schr\"{o}dinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well $V_{0}$ and $W$, the radial $n_{r}$ and $l$ orbital quantum numbers and parameters $D,a,R_{0}$ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a $^{56} Fe$ nucleus are calculated in $D=2$ and $D=3$, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of $D=2$ and $D=3$.

nucl-th↗