د. وجديقدح

قسم الفيزياء كلية العلوم

الاسم الكامل

د. وجدي عبد العزيز حميده قدح

المؤهل العلمي

دكتوراة

الدرجة العلمية

استاذ مساعد

ملخص

وجدي عبدالعزيز قـدح هو أحد أعضاء هيئة التدريس بقسم الفيزياء بكلية العلوم. بعـد حصوله على درجة الماجستير بتقدير إمتياز من جامعة طرابلس سنة 1993 (في مجال الفيزياء النووية) عـمل بمركز البحوث التقنية (قسم الليزر) ثم جامعة طرابلس ثم استكمل دراسته العليا بجامعة دارم ببريطانيا ( Durham University ) وتحصل منها على درجة الدكتوراة عام 2002 في مجالي فيزياء الجسيمات الاولية و الفيزياء الرياضية وقد عمل كمساعد محاضر مدة عامين تقريباً أثناء إقامته بجامعة دارم وبعد تخرجه عمل كباحث زائر في نفس الجامعة. وهو يعمل حالياً بدرجة أستاذ مساعد بقسم الفيزياء حيث يقوم بمهام البحث العلمي والتدريس للمرحلتين الجامعية و الدراسات العليا و له بعض المنشورات العالمية بمفرده في مجال الفيزياء الكمية التي تمثل أكبر اهتماماته العلمية الحالية.

معلومات الاتصال

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الاستشهادات

الكل منذ 2017
الإقتباسات
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المنشورات

Discrete symmetry approach to exact bound-state solutions for a regular hexagon Dirac billiard

We consider solving the stationary Dirac equation for a spin-1/2 fermion confined in a two dimension quantum billiard with a regular hexagon boundary, using symmetry transformations of the point group C6v. Closed-form bound-state solutions for this problem are obtained and the non-relativistic limit of our results are clearly discussed. Due to an adequate choice of confining boundary conditions the upper components of the planar Dirac-spinor eigenfunctions are shown to satisfy the corresponding hexagonal Schrödinger billiard, and the Dirac positive energy eigenvalues are proven to reduce directly to their Schrödinger counterparts in the non-relativistic limit. An illustrative application of our group theoretic method to the well-known square billiard problem has been explicitly provided. The success of our approach in solving equilateral-triangle, square and regular hexagon quantum billiards may well imply a possible applicability to other regular polygonal billiards. A quick look on nodal domains of the Schrödinger eigenfunctions for the hexagon billiard is also considered. Moreover, we have determined a number of distinct non-congruent polygonal billiards that have the same eigenvalue spectrum as that of the regular hexagon.
Wajdi A. Gaddah(4-2021)
Publisher's website


Exact solutions to the Dirac equation for equilateral triangular billiard systems

We present a simple analytical method, based on the symmetry transformations of the point group C3v, to derive the exact energy eigenvalues and eigenfunctions of the stationary Dirac equation for a spin-1/2 fermion confined in a quantum billiard of an equilateral triangular shape with impenetrable boundary. Adequate boundary conditions on the Dirac spinors are proposed to preserve the self-adjointness of the Dirac operator, and guarantee the impenetrability of the probability current through the hard walls of the triangular billiard. The non-relativistic limit of our results are calculated and found to be in full agreement with their corresponding counterparts in the Schrödinger wave mechanics.
Wajdi A. Gaddah(8-2018)
Publisher's website


A Lie group approach to the Schrödinger equation for a particle in an equilateral triangular infinite well

In this paper, we present Lie’s method of using one-parameter groups of continuous transformations to find the exact solution to the Schrödinger equation for a particle confined in an equilateral triangle. A suitable Lie group transformation that leaves the Schrödinger equation in the complex variable formulation invariant is determined by detection and then used to reduce the partial differential equation to an ordinary differential equation which admits the so-called group-invariant solution. This particular solution along with other symmetry transformations is used to generate the full solution that complies with Dirichlet boundary conditions. The eigenfunctions and eigenvalues obtained herein are in full agreement with those derived by other methods. Our approach has been presented in a simple manner in the hope that it will be beneficial at the undergraduate level.
Wajdi Abdulaziz Hameedah Gaddah(7-2013)
Publisher's website


A higher-order finite-difference approximation with Richardson’s extrapolation to the energy eigenvalues of the quartic, sextic and octic anharmonic oscillators

In this paper, we present highly accurate numerical results for the lowest four energy eigenvalues of the quartic, sextic and octic anharmonic oscillators over a wide range of the anharmonicity parameter λ. Also, we provide illustrative graphs describing the dependence of the eigenvalues on λ. Our computation is carried out by using higher-order finite-difference approximation, involving the nine-and-ten-point differentiation formulas. In addition, we apply Richardson’s extrapolation method in our calculation for the purpose of achieving a maximum numerical precision. The main advantage of utilizing the finite-difference approach lies in its simplicity and capability to transform the time-independent Schrödinger equation into an eigenvalue matrix equation. This allows the use of numerical matrix algebra for obtaining several eigenvalues and eigenvectors simultaneously without consuming much of the computer time. The method is illustrated in a simple pedagogical way through which the close relation between differential and algebraic eigenvalue problems are clearly seen. The findings of our computations via MATLAB are tested on a number of accurate results derived by different methods.
Wajdi Abdulaziz Hameedah Gaddah(4-2015)
Publisher's website


Borel Resummation Method with Conformal Mapping and the Ground State Energy of the Quartic Anharmonic Oscillator

In this paper, we consider the resummation of the divergent Rayleigh-Shrödinger perturbation expansion for the ground state energy of the quartic anharmonic oscillator in one dimension. We apply the Borel-Padé resummation method combined with a conformal mapping of the Borel plane to improve the accuracy and to enlarge the convergence domain of the perturbative expansion. This technique was recently used in perturbative QCD to accelerate the convergence of Borel-summed Green’s functions. In this framework, we calculated the ground state energy of the quartic anharmonic oscillator for various coupling constants and compared our results with the ones we obtained from the diagonal Padé approximation and the standard Borel resummation technique. The results are also tested on a number of exact numerical solutions available for weak and strong coupling constants. As a part of our calculations, we computed the coefficients of the first 50 correction terms in the Rayleigh- Shrödinger perturbation expansion using the method of Dalgarno and Stewart. The conformal mapping of the Borel plane is shown to enhance the power of Borel’s method of summability, especially in the strong coupling domain where perturbation theory is not applicable.
Wajdi A. Gaddah(4-2009)