124 citations · 309 across the 17 of their papers we have counts for
17 papers
Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries
M. H. Al-Hashimi, U. -J. Wiese
For a particle moving on a half-line or in an interval the operator is not self-adjoint and thus does not qualify as the physical momentum. Consequently c…
A New Concept for the Momentum of a Quantum Mechanical Particle in a Box
M. H. Al-Hashimi, U. -J. Wiese
For a particle in a box, the operator is not Hermitean. We provide an alternative construction of a momentum operator , which has a Hermitean comp…
Energy and Angular Momentum Dependent Potentials with Closed Orbits
Munir Al-Hashimi
The Bertrand theorem concluded that; the Kepler potential, and the isotropic harmonic oscillator potential are the only systems under which all the orbits are closed. It was never…
The General Solution for the Relativistic and Nonrelativistic Schrödinger Equation for the -Function Potential in 1-dimension Using Cutoff Regularization, and the Fate of Universality
M. H. Al-Hashimi, M. Salman, A. M. Shalaby
A general method has been developed to solve the Schrödinger equation for an arbitrary derivative of the -function potential in 1-d using cutoff regularization. The work treats…
Majorana Fermions in a Box
M. H. Al-Hashimi, A. M. Shalaby, U. -J. Wiese
Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical latti…
Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity
M. H. Al-Hashimi, A. M. Shalaby, U. -J. Wiese
The non-relativistic hydrogen atom enjoys an accidental symmetry, that enlarges the rotational symmetry, by extending the angular momentum algebra with the Runge-Le…
The Solution of the Relativistic Schrodinger Equation for the -Function Potential in 1-dimension Using Cutoff Regularization
M. H. Al-Hashimi, A. M. Shalaby
We study the relativistic version of Schrödinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularizati…
A Solution of the Relativistic Schrödinger Equation for the -Function Potential in 1-dimensiona with Cutoff Regularization
M. H. Al-Hashimi, Abouzeid M. Shalaby
We study the solution of the relativistic Schrödinger equation for a point particle in 1-d under -function potential by using cutoff regularization. We show that the problem is…
Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the -Function Potential in 1-dimensional Relativistic Quantum Mechanics
M. H. Al-Hashimi, A. M. Shalaby, U. -J. Wiese
We consider the Schrödinger equation for a relativistic point particle in an external 1-dimensional -function potential. Using dimensional regularization, we investigate both bo…
Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
M. H. Al-Hashimi, M. Salman, A. Shalaby +1
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While t…
Harmonic Oscillator in a 1D or 2D Cavity with General Perfectly Reflecting Walls
M. H. Al-Hashimi
We investigate the simple harmonic oscillator in a 1-d box, and the 2-d isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. Th…
Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone
M. H. Al-Hashimi, U. -J. Wiese
In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation…
From a Particle in a Box to the Uncertainty Relation in a Quantum Dot and to Reflecting Walls for Relativistic Fermions
M. H. Al-Hashimi, U. -J. Wiese
We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some c…
Minimal Position-Velocity Uncertainty Wave Packets in Relativistic and Non-relativistic Quantum Mechanics
U. -J. Wiese, M. H. Al-Hashimi
We consider wave packets of free particles with a general energy-momentum dispersion relation . The spreading of the wave packet is determined by the velocity $v = \p_p E$. T…
Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus
M. H. Al-Hashimi, U. -J. Wiese
A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to…
Runge-Lenz Vector, Accidental SU(2) Symmetry, and Unusual Multiplets for Motion on a Cone
M. H. Al-Hashimi, U. -J. Wiese
We consider a particle moving on a cone and bound to its tip by or harmonic oscillator potentials. When the deficit angle of the cone divided by is a rational number, a…
Discrete Momentum Mechanics and Faster Than Light Transition
Munir Al-Hashimi
In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesi…