arXiv subjects

Zeinab Algadhi

Publications and source records attributed to Zeinab Algadhi.

5 recordsLinked to original sources

arXiv2022

Position-dependent mass Schrödinger particles in space-like screw dislocation: associated degeneracies and magnetic and Aharonov-Bohm flux fields effects

We consider non-relativistic position-dependent mass (PDM) Schrodinger particles moving in an elastic medium with space-like screw dislocation. Within the cylindrical coordinates, we study and report the effects of screw dislocation as well as PDM settings on the energy levels of some PDM-quantum mechanical systems. In so doing, we use a power-law type positive-valued dimensionless scalar multiplier f(r) (Which manifestly introduces the metaphoric notion of PDM-Schrodinger particles). Next, we subject such PDM particles to magnetic and Aharonov-Bohm flux fields. We report exact or conditionally exact eigenvalues and eigenfunctions for V (r) = 0 and V (r) = a + b r + c r^2

quant-ph↗

arXiv2020

PDM-charged particles in PD-magnetic plus Aharonov-Bohm flux fields: unconfined "almost-quasi-free" and confined in a Yukawa plus Kratzer exact solvability

Using azimuthally symmetrized cylindrical coordinates, we consider some position-dependent mass (PDM) charged particles moving in position-dependent (PD) magnetic and Aharonov-Bohm flux fields. We focus our attention on PDM-charged particles (i.e., the PDM is only radially dependent) moving in an inverse power-law-type radial PD-magnetic fields. Under such settings, we consider two almost-quasi-free PDM-charged particles (i.e., no interaction potential). Both yield exactly solvable Schrödinger equations of Coulombic nature but with different spectroscopic structures. Moreover, we consider a Yukawa-type PDM-charged particle moving not only in the vicinity of the PD-magnetic and Aharonov-Bohm flux fields but also in the vicinity of a Yukawa plus a Kratzer type potential force field. For this particular case, we use the Nikiforov-Uvarov (NU) method to come out with exact analytical eigenvalues and eigenfunctions. Which, in turn, recover those of the almost-quasi-free PDM-charged particle. Energy levels crossings are also reported.

math-ph↗

arXiv2020

Landau Quantization for an electric quadrupole moment of Position-Dependent Mass Quantum Particles interacting with Electromagnetic fields

Analogous to Landau quantization related to a neutral particle possessing an electric quadrupole moment, we generalize such Landau quantization to include position-dependent mass (PDM) neutral particles. Using cylindrical coordinates, the exact solvability of PDM neutral particles with an electric quadrupole moment moving in electromagnetic fields is reported. The interaction between the electric quadrupole moment of a PDM neutral particle and a magnetic field in the absence of an electric field is analyzed for two different radial cylindrical PDM settings. Next, two particular cases of radial electric fields (E=λ\r{ho}/\r{ho} and E=λ\r{ho}/2\r{ho}) are considered to investigate their influence on the Landau quantization (of this system using the same models of PDM settings). The exact eigenvalues and eigenfunctions for each case are analytically obtained.

quant-ph↗

arXiv2019

Position-dependent mass charged particles in magnetic and Aharonov-Bohm flux fields: separability, exact and conditionally exact solvability

Using cylindrical coordinates, we consider position-dependent mass (PDM) charged particles moving under the influence of magnetic, Aharonov-Bohm flux, and a pseudoharmonic or a generalized Killingbeck-type potential fields. We implement the PDM-minimal-coupling recipe 26 , along with the PDM-momentum operator 27 , and report separability under radial cylindrical and azimuthal symmetrization settings. For the radial Schrödinger part, we transform it into a radial one-dimensional Schrödinger-type and use two PDM settings to report on the exact solvability of PDM charged particles moving in three fields: magnetic, Aharonov-Bohm flux, and pseudoharmonic potential fields. Next, we consider the radial Schrödinger part as is and use the biconfluent Heun differential forms for two PDM settings to report on the conditionally exact solvability of our PDM charged particles moving in three fields: magnetic, Aharonov-Bohm flux, and generalized Killingbeck potential fields. Yet, we report the spectral signatures of the one-dimensional z-dependent Schrödinger part on the overall eigenvalues and eigenfunctions, for all examples, using two z-dependent potential models (infinite potential well and Morse-type potentials).

math-ph↗

arXiv2018

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics, it admits a necessarily different and vital form in quantum mechanics. Under our point transformation settings, only one of the two commonly used vector potentialsis found eligible and is considered for our Illustrative examples.

math-ph↗