arXiv subjects

Sameer M. Ikhdair

Publications and source records attributed to Sameer M. Ikhdair.

At least 91 records · Page 5Linked to original sources

arXiv2009

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulthén potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.

quant-ph↗

arXiv2008

Bound states of the Klein-Gordon equation for vector and scalar general Hulthen-type potentials in D-dimension

We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulthén-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the calculations. We obtain the bound state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D=1 and 3 dimensions. Our results are valid for $q=1$ value when $l\neq 0$ and for any $q$ value when $l=0$ and D=1 or 3. The $s$% -wave ($l=0$) binding energies for a particle of rest mass $m_{0}=1$ are calculated for the three lower-lying states $(n=0,1,2)$ using pure vector and pure scalar potentials.

quant-ph↗

arXiv2008

Exactly solvable effective mass D-dimensional Schrodinger equation for pseudoharmonic and modified Kratzer problems

We employ the point canonical transformation (PCT) to solve the D-dimensional Schrödinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($D\geq 2$) Schrödinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.

quant-ph↗

arXiv2008

Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials

A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ bound-state solutions of the Schrödinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers $n$ and $l$ with two different values of the potential parameter $σ_{\text{0}}.$ Our numerical results are of high accuracy like the other numerical results obtained by using program based on a numerical integration procedure for short-range and long-range potentials. The energy bound-state solutions for the s-wave ($l=0$) and $σ_{0}=1$ cases are given.

quant-ph↗

arXiv2008

Solutions of Dirac Equation for Symmetric Generalized Woods-Saxon Potential by the Hypergeometric Method

The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $κ$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into a Schrödinger-like differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.

quant-ph↗

arXiv2008

Solution of the D-dimensional Klein-Gordon equation with equal scalar and vector ring-shaped pseudoharmonic potential

We present the exact solution of the Klein-Gordon equation in D-dimensions in the presence of the noncentral equal scalar and vector pseudoharmonic potential plus the new ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound-state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this noncentral ring-shaped pseudoharmonic potential can be reduced to the three-dimensional pseudoharmonic solution once the coupling constant of the noncentral part of the potential becomes zero.

quant-ph↗

arXiv2008

Exact Quantization Rule to the Kratzer-Type Potentials: An Application to the Diatomic Molecules

For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple exact analytical solution of the $D$-dimensional ($D\geq 2$) hyperradial Schr% ödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels $(E_{nl})$ of all the bound-states are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions $% (ψ_{nl}(r))$ are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for the typical diatomic molecules $LiH,$ $CH,$ $HCl,$ $CO,$ $NO,$ $O_{2},$ $N_{2}$ and $I_{2}$ for various values of $n$ and $l$ quantum numbers. Numerical tests using the energy calculations for the interdimensional degeneracy ($D=2-4$) for $I_{2}, $ $LiH,$ $HCl,$ $O_{2},$ $NO$ and $CO$ are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.

quant-ph↗

arXiv2008

Approximate l-state solutions of the Manning-Rosen potential by the Nikiforov-Uvarov method

The Schrodinger equation for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states energies. Additionally, the corresponding wave functions are expressed by the Jacobi polynomials. The Nikiforov-Uvarov (${\rm NU}$) method is used in the calculations. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers $n$ and $l$ with two different values of the potential parameter $α.$ It is shown that the results are in good agreement with the those obtained by other methods for short potential range, small $l$ and $α.$ This solution reduces to two cases $l=0$ and Hulthen potential case.

quant-ph↗

arXiv2008

Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential

The Schrödinger equation in $D$-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov(NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers $n$ and $l$ with three different values of the potential parameter $α.$ It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional sytem from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation $(n,l,D)\to (n,l\pm 1,D\mp 2)$. This solution reduces to the Hulthén potential case.

quant-ph↗

arXiv2007

Elativistic treatment in}$D$ - Dimensions to a spin-zero particle with noncentral equal scalar and vector ring-shaped Kratzer potential

The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the noncentral equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three-dimensions given by other works.

quant-ph↗

arXiv2007

Relativistic treatment in D-dimensions to a spin-zero particle with noncentral equal scalar and vector ring-shaped Kratzer potential

quant-ph↗

arXiv2007

Exact solutions of the Schrodinger equation in D-dimensions for the pseudoharmonic potential plus ring-shaped potential

We present analytically the exact energy bound-states solutions of the Schrodinger equation in $D$-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form $V(r,θ)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r}) ^{2}+\frac{β\cos ^{2}θ}{r^{2}\sin ^{2}θ}$ by means of the conventional Nikiforov-Uvarov method. We also give a clear recipe of how to obtain an explicit solution to the radial and angular parts of the wave functions in terms of orthogonal polynomials. The total energy of the system is different from the pseudoharmonic potential because of the contribution of the angular part. The general results obtained in this work can be reduced to the standard forms given in the literature.

quant-ph↗

arXiv2007

Exact solutions of the pseudo-Coulomb potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for an alternative (often used) pseudo-Coulomb potential-plus- ring-shaped potential of the form $V(r)=-% \frac{a}{r}+\frac{b}{r^{2}}+\frac{β\cos ^{2}θ}{r^{2}\sin ^{2}θ}+c$ by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the radial and angular parts of the wave functions in terms of orthogonal polynomials. The total energy of the system is different from the pseudo-Coulomb potential because of the contribution of the angular part. The general results obtained in this work can be reduced to the standard forms given in literature.

quant-ph↗

arXiv2007

Exact solutions of the modified Kratzer potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.

quant-ph↗

arXiv2007

An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in $D$-dimensions. We show that the perturbed Coulomb problem with eigenvalue $E$ can be transformed to a sextic anharmonic oscillator problem with eigenvalue E. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with $k=D+2\ell $ appearing in the wave equation satisfy certain constraints.

quant-ph↗

arXiv2007

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.

quant-ph↗

arXiv2007

Calculation of the B_{c}leptonic decay constant using the shifted N-expansion method

We give a review and present a comprehensive calculation for the leptonic constant B_{c} of the low-lying pseudoscalar and vector states of B_{c}-meson in the framework of static and QCD-motivated nonrelativistic potential models taking into account the one-loop and two-loop QCD corrections in the short distance coefficient that governs the leptonic constant of $B_{c}$ quarkonium system. Further, we use the scaling relation to predict the leptonic constant of the nS-states of the (b_bar)c system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

hep-ph↗

arXiv2007

Exact solutions of the radial Schrodinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and Kratzer potentials in two dimensions. The energy levels of all the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained.

quant-ph↗