arXiv subjects

Sameer M. Ikhdair

Publications and source records attributed to Sameer M. Ikhdair.

At least 37 records · Page 2Linked to original sources

arXiv2014

Nonrelativistic molecular models under external magnetic and AB flux fields

By using the wave function ansatz method, we study the energy eigenvalues and wave function for any arbitrary $m$-state in two-dimensional Schrödinger wave equation with various power interaction potentials in constant magnetic and Aharonov-Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We calculate the energy levels of some diatomic molecules in the presence and absence of external magnetic and AB flux fields using different potential models. We found that the effect of the Aharonov-Bohm field is much as it creates a wider shift for $m\neq 0$ and its influence on $m=0$ states is found to be greater than that of the magnetic field. To show the accuracy of the present model, a comparison is made with those ones obtained in the absence of external fields. An extension to 3-dimensional quantum system have also been presented.

quant-ph↗

arXiv2014

Formula Method for Bound State Problems

We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of $Ψ"(s)+\frac{(k_1-k_2s)}{s(1-k_3s)}Ψ'(s)+\frac{(As^2+Bs+C)}{s^2(1-k_3s)^2}Ψ(s)=0$. The two cases where $k_3=0$ and $k_3\neq 0$ are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions $_2F_1(α, β; γ; k_3s)$. In order to show the accuracy of this proposed formula, we resort to obtaining bound state solutions for some existing eigenvalue problems in a rather more simplified way. This method has been shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models.

math-ph↗

arXiv2014

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov-Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov-Uvarov (NU) method.

quant-ph↗

arXiv2013

Approximate Analytical Solutions to Relativistic and Nonrelativistic Pöschl-Teller Potential with its Thermodynamic Properties

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrodinger system. Rotational-Vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as s-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S.

quant-ph↗

arXiv2013

Approximate relativistic bound states of a particle in Yukawa field with Coulomb tensor interaction

We obtain the approximate relativistic bound state of a spin-1/2 particle in the field of the Yukawa potential and a Coulomb-like tensor interaction with arbitrary spin-orbit coupling number k under the spin and pseudospin (p-spin) symmetries. The asymptotic iteration method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms. Our numerical results show that the tensor interaction removes degeneracies between the spin and p-spin doublets and creates new degenerate doublets for various strengths of tensor coupling.

nucl-th↗

arXiv2013

Approximate eigensolutions of the deformed Woods-Saxon potential via AIM

By using the Pekeris approximation, the Schrödinger equation is solved for the nuclear deformed Woods-Saxon potential within the framework of the asymptotic iteration method (AIM). The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function.

quant-ph↗

arXiv2013

Spinless particles in the field of unequal Scalar-Vector Yukawa potentials

We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary -state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst energy states of the KG-Yukawa problem. The dependence of the energy on the dimension is numerically discussed for spatial dimensions

nucl-th↗

arXiv2013

Relativistic symmetries in Rosen-Morse potential and tensor interaction using the Nikiforov-Uvarov method

Approximate analytical bound-state solutions of the Dirac particle in the field of both attractive and repulsive RM potentials including Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number The Pekeris approximation is used to deal with the spin-orbit coupling terms In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov-Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between spin and p-spin state doublets.

quant-ph↗

arXiv2013

Relativistic symmetries in trigonometric Poschl-Teller potential plus tensor interaction

The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Poschl-Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit quantum number $κ$ using an approximation scheme to substitute the centrifugal terms k(k+1)/r^2. In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling $A$ and for various values of spin and p-spin constants and quantum numbers n and k. The non-relativistic limit is also obtained.

quant-ph↗

arXiv2013

Dirac bound state solutions of spherically ring-shaped q-deformed Woods-Saxon potential for any L-state

Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave function are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term L(L+1)/r^2. Under some limitations, we can obtain solution for the ring-shaped Hulthén potential and the standard usual spherical Woods-Saxon potential (q=1).

nucl-th↗

arXiv2013

Approximate relativistic solutions for a new ring-shaped Hulthén potential

Approximate bound state solutions of the Dirac equation with the Hulthén plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary -state. The energy eigenvalue equation and the corresponding two-component wave function are calculated by solving the radial and angular wave equations within a recently introduced shortcut of Nikiforov-Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are given in terms of the Jacobi polynomials. We use an exponential approximation in terms of the Hulthen potential parameters to deal with the strong singular centrifugal potential term Under the limiting case, the solution can be easily reduced to the solution of the Schrodinger equation with a new ring-shaped Hulthén potential.

quant-ph↗

arXiv2012

Duffin-Kemmer-Petiau particle in a vector exponential-like decaying field with any arbitrary -state

The Duffin Kemmer Petiau (DKP) equation is solved approximately for a vector exponential-like decaying potential with any arbitrary J state by using the Pekeris approximation. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in a closed form. The cases of zero total angular momentum and nonrelativistic limit are discussed too.

nucl-th↗

arXiv2012

Exact solutions of a spatially-dependent mass Dirac equation for Coulomb field plus tensor interaction via Laplace transformation method

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction

math-ph↗

arXiv2012

Relativistic new Yukawa-like potential and tensor coupling

We approximately solve the Dirac equation for a new suggested generalized inversely quadratic Yukawa (GIQY) potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number In the framework of the spin and pseudospin (p-spin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions, in closed form, by using the parametric Nikiforov-Uvarov (NU) method. The numerical results show that the Coulomb-like tensor interaction, removes degeneracies between spin and p-spin state doublets. The Dirac solutions in the presence of exact spin symmetry are reduced to Schrödinger solutions for Yukawa and inversely quadratic Yukawa potentials.

nucl-th↗

arXiv2012

Spectra of cylindrical quantum dots: the effect of electrical and magnetic fields together with AB flux field

We study the spectral properties of electron quantum dots (QDs) confined in 2D parabolic harmonic oscillator influenced by external uniform electrical and magnetic fields together with an Aharonov-Bohm (AB) flux field. We use the Nikiforov-Uvarov method in our calculations. Exact solutions for the energy levels and normalized wave functions are obtained for this exactly soluble quantum system. Based on the computed one-particle energetic spectrum and wave functions, the interband optical absorption GaAs spherical shape parabolic QDs is studied theoretically and the total optical absorption coefficient is calculated.

cond-mat.mes-hall↗

arXiv2012

A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for arbitrary -state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schrödinger-Woods-Saxon problem for arbitrary l -state and the exact s-wave (l=0).

nucl-th↗

arXiv2012

Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules

We obtain the bound-state solutions of the radial Schrödinger equation (SE) with the shifted Deng-Fan (sDF) oscillator potential in the frame of the Nikiforov-Uvarov (NU) method and employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding wave functions are obtained in closed form for arbitrary -state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

quant-ph↗

arXiv2012

Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector Pöschl-Teller (PT) potentials with arbitrary spin-orbit -wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of the hypergeometric functions are obtained by means of the wave function analysis. The spin- Dirac equation and the spin- Klein-Gordon (KG) equation with the complex Pöschl-Teller potentials share the same energy spectrum under the choice of (i.e., exact spin and p-spin symmetries).

quant-ph↗