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Ahmed Al-Jamel

Publications and source records attributed to Ahmed Al-Jamel.

10 recordsLinked to original sources
arXiv2024

Saturation effect in confined quantum systems with energy-dependent potentials

In this paper, we study the saturation effect in the energy or mass spectra of three quantum models with energy-dependent potentials: the harmonic oscillator, the hydrogen atom, and the heavy quarkonia. We used the method proposed in \cite{garcia2009exactly}, which is based on studying various canonical point and gauge transformations applied to a function, $g(x)$, multiplied by a given differential equation of known solutions as special orthogonal functions, that convert it into a Schr{ö}dinger-like equation. The first two models stem from implementing the method on the confluent hypergeometric differential of the well-known solutions ${}_1 F_1$, while the third model (heavy quarkonia) stems possibly from the hypergeometric differential of the well-known solutions ${}_2 F_1$. In particular, the heavy quarkonia mass spectra for both $c\bar c$ and $b\bar b$ are produced at different values of the saturation parameter $λ$ and compared with the available experimental data. It is found that these systems may exhibit saturation effect when the energy-dependent effect is included.

quant-ph↗
arXiv2024

Hard confinement of a two-particle quantum system using the variational method

The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wavefunction is constructed as the product of the $1S$ free hydrogen atom wavefunction or $1S$ free harmonic oscillator wavefunction times a cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius $z$. The behavior of $|ψ|^2$, the wavefunction at the origin (WFO), and the mean radius $\ev{r}$ are computed for different situations and compared for the two potential models.

quant-ph↗
arXiv2023

Quantization of the Bateman damping system with conformable derivative

In this work, the conformable Bateman Lagrangian for the damped harmonic oscillator system is proposed using the conformable derivative concept. In other words, the integer derivatives are replaced by conformable derivatives of order $α$ with $0<α\leq 1$. The corresponding conformable Euler-Lagrange equations of motion and fractional Hamiltonian are then obtained. The system is then canonically quantized and the conformable Schrodinger equation is constructed. The fractional-order dependence of the energy eigenvalues $E_n ^α$ and eigenfunctions $ψ_n ^α$ are obtained using using suitable transformations and the extended fractional Nikiforov-Uvarov method. The corresponding conformable continuity equation is also derived and the probability density and probability current are thus suitably defined. The probability density evolution as well as its dependence on $α$ is plotted and analyzed for various situations. It is found that the energy eigenvalues are real and there are sort of gradual ordering in the behavior of the probability densities.

quant-ph↗
arXiv2021

The solution of conformable Laguerre differential equation using conformable Laplace transform

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of properties of the Laguerre polynomial is discussed and the conformable Rodriguez's Formula and generating function are proposed and proved

math.CA↗
arXiv2021

The effect of deformation of special relativity by conformable derivative

In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, and the conformable Gordon-Klein equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

physics.class-ph↗
arXiv2021

WKB Approximation with Conformable Operator

In this paper, the WKB method is extended to be applicable for conformable Hamiltonian systems where the concept of conformable operator with fractional order $α$ is used. The WKB approximation for the $α$-wavefunction is derived when the potential is slowly varying in space. The paper is furnished with some illustrative examples to demonstrate the method. The quantities of the conformable form are found to be inexact agreement with traditional quantities when $α=1$.

quant-ph↗
arXiv2019

Response to: [Comment on Quantization of the damped harmonic oscillator [Serhan et al, J. Math. Phys. 59, 082105 (2018)]]

This is a response to a recently reported comment [1] on paper [J. Math. Phys.59, 082105 (2018)] regarding the quantization of damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of [2] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be firstly achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. Applying the canonical quantization on the resulted Hermitian Hamiltonian and then using the Nikiforov-Uvarov method correctly, the energy eigenvalues will be real and exactly as given by Eq. (35) of [2].

quant-ph↗
arXiv2019

Heavy quarkonia properties from a hard-wall confinement potential model with conformal symmetry perturbing effects

Heavy $c\bar c$ and $b\bar b $ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent-- with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov-Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status of conformal symmetry in the heavy flavor sector. The resulting predictions on heavy quarkonia mass spectra and root mean square radii are compared with the available experimental data, as well as with predictions by other theoretical approaches. We observe that a relatively small conformal symmetry perturbing term in the potential suffices to achieve good agreement with data.

hep-ph↗
arXiv2015

Generalized relativistic anisotropic models for compact stars

We present new anisotropic generalization of Buchdahl [1] type perfect fluid solution by using the method of earlier work [2]. In similar approach we have constructed the new pressure anisotropy factor $Δ$ by the help both the metric potential $e^λ$ and $e^ν$. The metric potential $e^λ$ same as Buchdahl [1] and $e^ν$ is monotonic increasing function as suggested by Lake [3]. After that we obtain new well behaved general solution for anisotropic fluid distribution. We calculated the physical quantities like energy density, radial and tangential pressures, velocity of sound and red-shift etc. We observe that these quantities are positive and finite inside the compact star. Also note that mass and radius of our models can represent the structure of realistic astrophysical objects such as like Her X-1 and RXJ1856-37.

gr-qc↗