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Dhahran, Saudi Arabia

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. Source


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. Source


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. Source


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. Source


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. Source

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