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Omar Mustafa

Publications and source records attributed to Omar Mustafa.

At least 73 records · Page 4Linked to original sources
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↗
arXiv2020

PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian

The exact solvability and impressive pedagogical implementation of the harmonic oscillator creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the position dependent mass oscillator for the position dependent mass quantum mechanics. We, hereby, construct the position dependent mass creation and annihilation operators for the position dependent mass oscillator via two different approaches. First, via von Roos position dependent mass Hamiltonian and show that the commutation relation between the position dependent mass creation and annihilation operators not only offers a unique position dependent mass Hamiltonian but also suggests a position dependent mass deformation in the coordinate system. Next, we use a position dependent mass point canonical transformation of the textbook constant mass harmonic oscillator analog and obtain yet another set of position dependent mass creation and annihilation operators, hence an apparently new position dependent mass Hamiltonian is obtained. The new position dependent mass Hamiltonian turned out to be not only correlated but also represents an alternative and most simplistic user-friendly position dependent mass Hamiltonian that has never been reported before.

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↗
arXiv2019

On the n-dimensional extension of Position-dependent mass Lagrangians: nonlocal transformations, Euler--Lagrange invariance and exact solvability

The n-dimensional extension of the one dimensional Position-dependent mass (PDM) Lagrangians under the nonlocal point transformations by Mustafa 38 is introduced. The invariance of the n-dimensional PDM Euler-Lagrange equations is examined using two possible/different PDM Lagrangian settings. Under the nonlocal point transformation of Mustafa 38 , we have shown that the PDM Euler-Lagrange invariance is only feasible for one particular PDM-Lagrangians settings. Namely, when each velocity component is deformed by some dimensionless scalar multiplier that renders the mass position-dependent. Two illustrative examples are used as reference Lagrangians for different PDM settings, the nonlinear n-dimensional PDM-oscillators and the nonlinear isotonic n-dimensional PDM-oscillators. Exact solvability is also indulged in the process.

math-ph↗
arXiv2019

Comment on 'Two-dimensional position-dependent massive particles in the presence of magnetic fields"

Using the well known position-dependent mass (PDM) von Roos Hamiltonian, Dutra and Oliveira (2009 J. Phys. A: Math. Theor. 42 025304) have studied the problem of two-dimensional PDM particles in the presence of magnetic fields. They have reported exact solutions for the wavefunctions and energies. In the first part of their study "PDM-Shrödinger equation in two-dimensional Cartesian coordinates", they have used the so called Zhu and Kroemer's ordering α=-1/2=γ and \b{eta}=0 5 . While their treatment for this part is correct beyond doubt, their treatment of second part "PDM in a magnetic field" is improper . We address these improper treatments and report the correct presentation for minimal coupling under PDM settings.

quant-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↗
arXiv2017

Two-dimensional position-dependent mass Lagrangians; Superintegrability and exact solvability

The two-dimensional extension of the one-dimensional PDM-Lagrangians and their nonlocal point transformation mappings into constant unit-mass exactly solvable Lagrangians is introduced. The conditions on the related two-dimensional Euler-Lagrange equations' invariance are reported. The mappings from superintegrable linear oscillators into sub-superintegrable nonlinear PDM-oscillators are exemplified by, (i) a sub-superintegrable Mathews-Lakshmanan type-I PDM-oscillator, for a PDM-particle moving in a harmonic oscillator potential, (ii) a sub-superintegrable Mathews-Lakshmanan type-II PDM-oscillator, for a PDM-particle moving in a constant potential, and (iii) a sub-superintegrable shifted Mathews-Lakshmanan type-III PDM-oscillator, for a PDM-particle moving in a shifted harmonic oscillator potential. Moreover, the superintegrable shifted linear oscillators and the isotonic oscillators are mapped into a sub-superintegrable PDM-nonlinear and a sub-superintegrable PDM-isotonic oscillators, respectively.

math-ph↗
arXiv2015

Position-dependent mass Lagrangians: nonlocal transformations, Euler-Lagrange invariance and exact solvability

A general non-local point transformation for position-dependent mass Lagrangians and their mapping into a "constant unit-mass" Lagrangians in the generalized coordinates is introduced. The conditions on the invariance of the related Euler-Lagrange equations are reported. The harmonic oscillator linearization of the PDM Euler-Lagrange equations is discussed through some illustrative examples including harmonic oscillators, shifted harmonic oscillators, a quadratic nonlinear oscillator, and a Morse-type oscillator. The Mathews-Lakshmanan nonlinear oscillators are reproduced and some "shifted" Mathews-Lakshmanan nonlinear oscillators are reported. The mapping of an isotonic nonlinear oscillator into a PDM deformed isotonic oscillator is also discussed.

math-ph↗
arXiv2015

A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic molecules

We suggest a new deformed Schioberg-type potential for diatomic molecules. We show that it is equivalent to Tietz-Hua oscillator potential. We discuss how to relate our deformed Schiöberg potential to Morse, to Deng-Fan , to the improved Manning-Rosen, and to the deformed modified Rosen-Morse potential models. We transform our potential into a proper form and use the supersymmetric quantization to find a closed form analytical solution for the ro-vibrational energy levels that are highly accurate over a wide range of vibrational and rotational quantum numbers. We discuss our results using 4-diatomic molecules NO, O2, O2+, and N2. Our results turn out to compare excellently with those from a generalized pseudospectral numerical method.

math-ph↗
arXiv2015

On the ro-vibrational energies for the lithium dimer; maximum-possible rotational levels

The Deng-Fan potential is used to discuss the reliability of the improved Greene-Aldrich approximation and the factorization recipe of Badawi et al.'s [17] for the central attractive/repulsive core. The factorization recipe is shown to be a more reliable approximation and is used to obtain the ro-vibrational energies for the lithium dimer. For each vibrational state only a limited number of the rotational levels are found to be supported by the lithium dimer.

physics.chem-ph↗
arXiv2013

Classical and quantum quasi-free position dependent mass; Pöschl-Teller and ordering-ambiguity

We argue that the classical and quantum mechanical correspondence may play a basic role in the fixation of the ordering-ambiguity parameters. We use quasi-free position-dependent masses in the classical and quantum frameworks. The effective Pöschl-Teller model is used as a manifested reference potential to elaborate on the reliability of the ordering-ambiguity parameters available in the literature.

quant-ph↗
arXiv2013

On the nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator: Lagrange and Newton equations' equivalence

Using a generalized coordinate along with a proper invertible coordinate transformation, we show that the Euler-Lagrange equation used by Bagchi et al. 16 is in clear violation of the Hamilton's principle. We also show that Newton's equation of motion they have used is not in a form that satisfies the dynamics of position-dependent mass (PDM) settings.. The equivalence between Euler-Lagrange's and Newton's equations is now proved and documented through the proper invertible coordinate transformation and the introduction of a new PDM byproducted reaction-type force. The total mechanical energy for the PDM is shown to be conservative (i.e., dE/dt=0, unlike Bagchi et al.'s 16 observation).

physics.class-ph↗
arXiv2013

Position-dependent mass harmonic oscillator: classical-quantum mechanical correspondence and ordering-ambiguity

We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical and quantum position-dependent mass (PDM) oscillators. To elaborate on the ordering ambiguity, we properly amend some of the results reported in their work and discuss the classical and quantum mechanical correspondence for the PDM harmonic oscillators. We use a point canonical transformation and show that one unique quantum PDM oscillator Hamiltonian (consequently, one unique ordering-ambiguity parametric set j=l=-1/4 and k=-1/2) is obtained. To show that such a parametric set is not just a manifestation of the quantum PDM oscillator Hamiltonian, we consider the classical and quantum mechanical correspondence for quasi-free PDM particles moving under the influence of their own PDM force fields.

quant-ph↗
arXiv2013

(1+1)-Dirac bound states in one-dimension; position-dependent Fermi velocity and mass

We extend Panella and Roy's [13] work on one-dimensional heterostructure for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where both the mass and velocity are position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PD-mass and PD-velocity that satisfy the condition m(x)v(x)v(x)=A, where A is constant. (1+1)-Dirac Poschl-Teller and harmonic oscillator models are also reported.

math-ph↗
arXiv2012

Auxiliary quantization constraints on the von Roos ordering-ambiguity at zero binding energies; azimuthally symmetrized cylindrical coordinates

Using azimuthally symmetrized cylindrical coordinates, we report the consequences of zero-energy quantal states on the von Roos Hamiltonian. A position-dependent mass M(ρ,ϕ,z)=bz^{j}ρ^{2\u{psion}+1}/2 is used. We show that the zero-energy setting not only offers an additional degree of freedom towards feasible separability for the von Roos Hamiltonian, but also manifestly yields auxiliary quantized ambiguity parametric constraints.

quant-ph↗
arXiv2011

On Dirac equation for a Coulomb scalar, vector, and tensor interaction

In their recent paper (Inter. J. Mod. Phys. A 26 (2011) 1011), Zarrinkamar and coauthors have considered the radial Dirac equation for a Coulomb scalar, vector and tensor interaction. The exact solutions for the energy eigenvalues they have reported for spin-symmetry and pseudo-spin symmetry were mishandled and are incorrect eigenvalues, therefore.

quant-ph↗
arXiv2011

Radial power-law position-dependent mass; Cylindrical coordinates, separability, and spectral signatures

We discuss the separability of the position-dependent mass Hamiltonian in cylindrical coordinates in the framework of a radial power-law position-dependent mass. We consider two particular radial mass settings; a harmonic oscillator type, and a Coulombic type. We subject the radial harmonic oscillator type mass to a radial harmonic oscillator potential and the radial Coulombic mass to a radial Coulombic potential. Azimuthal symmetry is assumed and spectral signatures of various z-dependent interaction potentials are reported.

quant-ph↗