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Sameer M. Ikhdair

Publications and source records attributed to Sameer M. Ikhdair.

At least 109 records · Page 6Linked to original sources
arXiv2007

On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz

Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the parameters of the given potential, $δ$ and $η$ are also given, where $η$ depends on a linear combination of the angular momentum quantum number $\ell $ and the spatial dimensions $D$ and $δ$ is a parameter in the ansatz to the wave function. On inserting D=3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

quant-ph↗
arXiv2006

Exact Polynomial Eigensolutions of the Schrodinger Equation for the Pseudoharmonic Potential

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By a proper transformation, this problem is also solved very simply by using the known eigensolutions of anharmonic oscillator potential.

quant-ph↗
arXiv2006

Exact Polynomial Solutions of the Mie-Type Potential in the N-Dimensional Schrodinger Equation

The polynomial solution of the N-dimensional space Schrodinger equation for a special case of Mie potential is obtained for any arbitrary $% l-state. The exact bound-state energy eigenvalues and the corresponding eigenfunctions are calculated for diatomic molecular systems in the Mie-type potential. Keywords: Mie potential, Schrodinger equation, Eigenvalue, Eigenfunction, Diatomic molecules

quant-ph↗
arXiv2006

Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method

The one-dimensional Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov(NU} method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.

quant-ph↗
arXiv2006

Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method

The one-dimensional spinless Salpeter equation has been solved for the PT-symmetric generalized Hulthén potential. The Nikiforov-Uvarov {NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthen potentials.

quant-ph↗
arXiv2006

Series Solutions of the N-Dimensional Position-Dependent Mass Schrodinger Equation with a General Class of Potentials

The analytical solutions of the N-dimensional Schrodinger equation with position-dependent mass for a general class of central potentials is obtained via the series expansion method. The position-dependent mass is expanded in series about origin. As a special case, the analytical bound-state series solutions and the recursion relation of the linear-plus-Coulomb (Cornell) potential with the decaying position-dependent mass m=m_{0}e^{-λr} are also found.

quant-ph↗
arXiv2006

Bound energy for the exponential-cosine-screened Coulomb potential

An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energıes for various eigenstates and the corresponding wave functions are obtained analytically up to the second perturbation term.

quant-ph↗
arXiv2006

Bound states of a more general exponential screened Coulomb potential

An alternative approximation scheme has been used in solving the Schrodinger equation to the more general case of exponential screened Coulomb potential, V(r)=-(a/r)\[1+(1+br)e^{-2br}]. The bound state energies of the 1s, $2s, and 3s-states, together with the ground state wave function are obtained analytically upto the second perturbation term.

quant-ph↗
arXiv2006

A perturbative treatment for the bound states of the Hellmann potential

A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-δr)/r$ of arbitrary strength $b$ and screening parameter $δ$. Although the analytic expressions for the energy eigenvalues $E_{n,l\text{}}$ yield quite accurate results for a wide range of $n,\ell $ in the limit of very weak screening, the results become gradually worse as the strength $b$ and the screening coefficient $δ$ increase. This is because that the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels.

quant-ph↗
arXiv2005

A perturbative treatment for the energy levels of neutral atoms

Energy levels of neutral atoms have been re-examined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number $Z$ up to 84 and compare very well with those obtained within the framework of hyper-virial-Pade scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

quant-ph↗
arXiv2005

A Systematic Study on Nonrelativistic Quarkonium Interaction

recently proposed strictly phenomenological static quark-antiquark potential belonging to the generality $V(r)=-Ar^{-α}+κr^β+V_{0}$ is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the $c\bar{c},$ $b\bar{b}$ and $c% \bar{b}$ quarkonia within a few ${\rm MeV}$ and also the five experimentally known leptonic decay widths of the $c\bar{c}$ and $b% \bar{b}$ vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. We give predictions for not yet observed $B_{c}$ splittings. The model is then used to predict the masses of the remaining quarkonia and the leptonic decay widths of the two pseudoscalar $c\bar{b%}$ states. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

hep-ph↗
arXiv2005

Exact Eigenvalues and Eigenfunctions of the Hulthen Potential in the PT-Symmetry for Any Angular Momentum

The Schrodinger equation with the PT-symmetric Hulthen potential is solved exactly by taking into account effect of the centrifugal barrier for any l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. Our numerical results are in good agreement with the ones obtained before. Keywords: Energy Eigenvalues and Eigenfunctions; Hulthen potential; PT-symmetry; Nikiforov-Uvarov Method.

quant-ph↗
arXiv2005

Polynomial Solution of PT-/Non-PT-Symmetric and Non-Hermitian Generalized Woods-Saxon Potential via Nikiforov-Uvarov Method

Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.

quant-ph↗
arXiv2005

Bound Energy Masses of Mesons Containing the Fourth Generation and Iso-singlet Quarks

The fourth Standard Model (SM) family quarks and weak iso-singlet quarks The fourth Standard Model (SM) family quarks and weak iso-singlet quarks predicted by ${\rm E}_{6\text{}}$ GUT are considered. The spin-average of the pseudoscalar $η_{4}(n^{1}S_{0})$ and vector $ψ_{4}(n^{3}S_{1})$ quarkonium binding masses of the new mesons formed by the fourth Standard Model (SM) family and iso-singlet ${\rm E}_{6\text{}}$ with their mixings to ordinary quarks are investigated. Further, the fine and hyperfine mass splittings of the these states are also calculated. We solved the Schrödinger equation with logarithmic and Martin potentials using the Shifted large-${\rm N}$ expansion technique. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

hep-ph↗
arXiv2005

Theoretical Status of the $B_{c}$ Meson in the Shifted l-Expansion Technique

In the framework of phenomenological static and QCD-motivated model potentials for heavy quarkonium, we compute the $\bar{b}c$ mass spectrum as well as its $\QTR{rm}{1S}$ hyperfine splitting using the recently introduced shifted $l$- expansion technique. We also predict the leptonic constant \ $f_{B_{c}}$ of the lightest pseudoscalar $B_{c}$ and $f_{B_{c}^{\ast}}$ of the vector $B_{c}^{\ast}$ states taking into account the one-loop and two-loop QCD corrections. Further, we use the scaling relation to predict the leptonic constant of the R{rm}{nS}$-states of the $\bar{b}c$ system. For the sake of comparison, we use the same fitting parameters of our previous model potentials. From our results we conclude that shifted $l$-expansion method has the same accuracy, convergence and status as our previous work.

hep-ph↗
arXiv2005

On the B_{c} leptonic decay constant

We give a review and present a comprehensive calculations 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 $\bar{b%}c$ system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

hep-ph↗
arXiv2004

B_{c} and heavy meson spectroscopy in the local approximation of the Schrodinger equation with relativistic kinematics

We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The pseudoscalar and vector decay constants of the $B_{c}$ meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form $% V(r)=-Ar^{-β}+κr^β+V_{0},$ with $β=1,1/2,~3/4$ which can also be decomposed into scalar and vector parts in the form $% V_{V}(r)=-Ar^{-β}+(1-ε)κr^β$ and $% V_{S}(r)=εκr^β+V_{0};$ where $0\leq ε\leq 1.$ The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.

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