880 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Saudi Center for Theoretical PhysicsSA54 papers
- Chouaib Doukkali UniversityMA33 papers
- King Abdullah University of Science and TechnologySA29 papers
- Massachusetts Institute of TechnologyUS17 papers
- Georgia Institute of TechnologyUS16 papers
- King Faisal UniversitySA12 papers
- Shura CouncilSA11 papers
- National University of SingaporeSG9 papers
- Northeastern UniversityUS9 papers
- Academy of Sciences Republic of UzbekistanUZ7 papers
- National University of Sciences and TechnologyPK7 papers
- Quaid-i-Azam UniversityPK7 papers
26 papers · 1 filter
J-matrix method of scattering for inverse-square singular potentials with supercritical coupling II. Regularization
Abdulaziz D. Alhaidari, Hocine Bahlouli, S. M. Al-Marzoug +1
This paper is a continuation of the previous one [Journal xx, xxxxx (2022)]. Here, we reformulate the same J-matrix theory by regularizing the inverse square singular potential. Th…
Bound states and the potential parameter spectrum
A. D. Alhaidari, H. Bahlouli
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound s…
Exact solvability of two new 3D and 1D nonrelativistic potentials within the TRA framework
I. A. Assi, H. Bahlouli, A. Hamdan
This work is concerned about introducing two new 1D and 3D confined potentials and present their solutions using the Tridiagonal Representation Approach (TRA). The wavefunction is…
A Functorial Construction of Quantum Subtheories
Ivan Contreras, Ali Nabi Duman
We apply the geometric quantization procedure via symplectic groupoids proposed by E. Hawkins to the setting of epistemically restricted toy theories formalized by Spekkens. In the…
Geometric Quantization and Epistemically Restricted Theories: The Continuous Case
Ivan Contreras, Ali Nabi Duman
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have ab…
Extending the class of solutions of the Dirac equation using tridiagonal matrix representations
A. D. Alhaidari, H. Bahlouli, I. A. Assi
The aim of this work is to find exact solutions of the one-dimensional Dirac equation that do not belong to the already known conventional class. We write the spinor wavefunction a…
Factorization of Dirac Equation in Two Space Dimensions
Hocine Bahlouli, Ahmed Jellal, Youness Zahidi
We present a systematic approach for the separation of variables for the two-dimensional Dirac equation in polar coordinates. The three vector potential, which couple to the Dirac…
The Dirac-Coulomb Problem: a mathematical revisit
A. D. Alhaidari, H. Bahlouli, M. E. H. Ismail
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with D…
Polynomial solutions of certain differential equations arising in physics
H. Azad, A. Laradji, M. T. Mustafa
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solu…
Extending the class of solvable potentials: III. The hyperbolic single wave
H. Bahlouli, A. D. Alhaidari
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schrödinger equation in terms of square integrable basis. The main characterist…
Extending the class of solvable potentials: II. Screened Coulomb potential with a barrier
A. D. Alhaidari
This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrab…
Dirac equation with coupling to 1/r singular vector potentials for all angular momenta
A. D. Alhaidari
We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is…
J-matrix method of scattering in one dimension: The nonrelativistic theory
A. D. Alhaidari, H. Bahlouli, M. S. Abdelmonem
We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well r…
Relativistic Double Barrier Problem with Three Sub-Barrier Transmission Resonance Regions
A. D. Alhaidari, H. Bahlouli, A. Jellal
We obtain exact scattering solutions of the Dirac equation in 1+1 dimensions for a double square barrier vector potential. The potential floor between the two barriers is higher th…
On the Exponential Decay of the n-point Correlation Functions and the Analyticity of the Pressure
Assane Lo
The goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n-point correlation functions for certain unbounded models of Kac type. The…
New method for evaluating integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example
A. D. Alhaidari
Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrat…
L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
A. D. Alhaidari
We obtain solutions of the three dimensional Dirac equation for radial power-law potentials at rest mass energy as an infinite series of square integrable functions. These are writ…
L2 series solution of the relativistic Dirac-Morse problem for all energies
A. D. Alhaidari
We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energ…
Studying resonance in the complex charge plane
A. D. Alhaidari
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing the…
Solution of the Dirac equation with position-dependent mass in the Coulomb field
A. D. Alhaidari
We obtain exact solution of the Dirac equation for a charged particle with position-dependent mass in the Coulomb field. The effective mass of the spinor has a relativistic compone…
Solution of the Dirac Equation for Potential Interaction
A. D. Alhaidari
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated…
Deformation of the three-term recursion relation and the generation of new orthogonal polynomials
A. D. Alhaidari
We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed rela…
Deformation of the J-matrix method of scattering
A. D. Alhaidari
We construct nonrelativistic J-matrix theory of scattering for a system whose reference Hamiltonian is enhanced by one-parameter linear deformation to account for nontrivial physic…
Scattering phase shift for relativistic exponential-type separable potentials
A. D. Alhaidari
The J-matrix method of scattering is used to obtain analytic expressions for the phase shift of two classes of relativistic exponential-type separable potentials whose radial compo…