Dhahran, Saudi Arabia
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Alhaidari A.D.,Saudi Center for Theoretical Physics | Alhaidari A.D.,King Fahd University of Petroleum and Minerals
International Journal of Modern Physics A | Year: 2010

We propose a relativistic one-parameter Hermitian theory for the Coulomb problem with an electric charge greater than 137. In the nonrelativistic limit, the theory becomes identical to the SchrödingerCoulomb problem for all Z. Moreover, it agrees with the DiracCoulomb problem to order (αZ) 2, where α is the fine structure constant. The vacuum in the theory is stable and does not suffer from the "charged vacuum" problem for all Z. Moreover, transition between positive and negative energy states could be eliminated. The relativistic bound states energy spectrum and corresponding spinor wave functions are obtained. © 2010 World Scientific Publishing Company.


Alhaidari A.D.,Saudi Center for Theoretical Physics | Alhaidari A.D.,King Fahd University of Petroleum and Minerals
Physica Scripta | Year: 2010

This is the second paper 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 integrable basis that carries a tridiagonal matrix representation of the wave operator. Consequently, the wave equation becomes equivalent to a three-term recursion relation for the expansion coefficients of the wavefunction in the basis. Finding solutions of the recursion relation is equivalent to solving the original problem. This method gives a larger class of solvable potentials. The usual diagonal representation constraint results in a reduction to the conventional class of solvable potentials. However, the tridiagonal requirement allows only very few and special potentials to be added to the solvability class. In the present work, we obtain S-wave solutions for a three-parameter 1/r singular but short-range potential with a nonorbital barrier and study its energy spectrum. We argue that it could be used as a more appropriate model for the screened Coulomb interaction of an electron with extended molecules. We give also its resonance structure for nonzero angular momentum. Additionally, we plot the phase shift for an electron scattering off a molecule modeled by a set of values of the potential parameters. © 2010 The Royal Swedish Academy of Sciences.


Khare A.,Indian Institute of Science | Al-Marzoug S.M.,King Fahd University of Petroleum and Minerals | Al-Marzoug S.M.,Saudi Center for Theoretical Physics | Bahlouli H.,King Fahd University of Petroleum and Minerals | Bahlouli H.,Saudi Center for Theoretical Physics
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2012

We investigate the effect of competing nonlinearities on beam dynamics in PT-symmetric potentials. In particular, we consider the stationary nonlinear Schrödinger equation (NLSE) in one dimension with competing cubic and generalized nonlinearity in the presence of a PT-symmetric potential. Closed form solutions for localized states are obtained. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow associated with these complex solitons is also examined. © 2012 Elsevier B.V.


Alhaidari A.D.,Saudi Center for Theoretical Physics | Alhaidari A.D.,King Fahd University of Petroleum and Minerals
Foundations of Physics | Year: 2010

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 obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and Eckart potentials. © 2010 Springer Science+Business Media, LLC.


Alhaidari A.D.,Saudi Center for Theoretical Physics
Physica Scripta | Year: 2011

We present a resolution of the Klein paradox within the framework of one-particle relativistic quantum mechanics. Not only reflection becomes total but the vacuum remains neutral as well. This is accomplished by replacing the physical pair production process with virtual negative energy 'incidence' within the barrier in a similar manner to what is done with virtual sources in optics and image charges in electrostatics. © 2011 The Royal Swedish Academy of Sciences.


Alhaidari A.D.,Saudi Center for Theoretical Physics
AIP Conference Proceedings | Year: 2011

We derive an elegant analytic formula for the energy spectrum of the relativistic Dirac-Morse problem. In the nonrelativistic limit, it reproduces the well-known result. This finding is significant when using the Morse potential as a model to describe the vibrational spectrum of diatomic and polyatomic molecules at strong coupling. © 2011 American Institute of Physics.


Alhaidari A.D.,Saudi Center for Theoretical Physics
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2011

We consider the Dirac equation in 1+1 space-time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples. © 2011 Elsevier B.V.


Alhaidari A.D.,Saudi Center for Theoretical Physics
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2013

We present a large class of non-Hermitian non-PT-symmetric two-component Dirac Hamiltonians with real energy spectra. Illustrative examples are given in 1+1 space-time of such systems with localized and/or continuum states. © 2013 Elsevier B.V. All rights reserved.


Alhaidari A.D.,Saudi Center for Theoretical Physics
International Journal of Theoretical Physics | Year: 2014

Nonlinear Dirac equations are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 space-time, we show that these requirements result in the "conventional" quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We consider the spin and pseudo-spin symmetric models and obtain a numerical solution. We also propose a two-component "minimal" pseudo-scalar coupling model. © 2013 Springer Science+Business Media New York.


Alhaidari A.D.,Saudi Center for Theoretical Physics
Journal of Mathematical Physics | Year: 2011

We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M - 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method. © 2011 American Institute of Physics.

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