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Sami I. Muslih

Publications and source records attributed to Sami I. Muslih.

At least 19 recordsLinked to original sources
arXiv2023

Conformable Schrödinger Equation in D-dimensional space

In this work, we extend the time-dependent conformable Schrödinger equation for a fractional dimensional system of N spatial coordinates to be used as an effective description of anisotropic and confined systems. A specific example is looked at in free particle conformable Schrödinger wave mechanics, particularly in N-Polar coordinates and N-Cartesian coordinates systems. The quantities of the conformable form are found to be in exact agreement with the corresponding traditional quantities when $β=1$

quant-ph↗
arXiv2023

Solving conformable Gegenbauer differential equation and exploring its generating function

In this manuscript, we address the resolution of conformable Gegenbauer differential equations. We demonstrate that our solution aligns precisely with the results obtained through the power series approach. Furthermore, we delve into the investigation and validation of various properties and recursive relationships associated with Gegenbauer functions. Additionally, we introduce and substantiate the conformable Rodriguez's formula and generating function

math.CA↗
arXiv2022

A formulation of Noether's theorem for fractional classical fields

This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a fractional action $S$, we obtain the fractional Euler-Lagrange equations of motion. Considerations of the Noether's variational problem for discrete systems whose action is invariant under gauge transformations will be extended to fractional variational problems for classical fields. The conservation laws associated with fractional classical fields are derived. As an example we present the conservation laws for the fractional Dirac fields.

math-ph↗
arXiv2010

Solutions of a particle with fractional $δ$-potential in a fractional dimensional space

A Fourier transformation in a fractional dimensional space of order $\la$ ($0<\la\leq 1$) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order $\a$. This new method is applied for a particle in a fractional $δ$-potential well defined by $V(x) =- γδ^{\la}(x)$, where $γ>0$ and $δ^{\la}(x)$ is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if $0< \la<\a$. The results for $\la= 1$ and $\a=2$ are in exact agreement with those presented in the standard quantum mechanics.

math-ph↗
arXiv2007

On fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a given classical Lagrangian or by multiplying with a constant the Lagrangian we obtain the same equations of motion. In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann-Liouville fractional derivatives. As a consequence of applying this procedure the classical results are reobtained as a special case. The fractional generalization of $Fa\grave{a}$ di Bruno formula is used in order to obtain the concrete expression of the fractional Lagrangians which differs from a given fractional Lagrangian by adding a fractional derivative. The fractional Euler-Lagrange and Hamilton equations corresponding to the obtained fractional Lagrangians are investigated and two examples are analyzed in details.

math-ph↗
arXiv2007

Fractional WKB Approximation

Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as the Hamilton's principle function "S". To demonstrate our proposed approach two examples are investigated in details.

math-ph↗
arXiv2006

Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.

math-ph↗
arXiv2004

Hamilton-Jacobi quantization of singular Lagrangians with linear velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.

hep-th↗
arXiv2003

Completely and Partially Integrable Systems of Total Differential Equations

Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it Partially integrable systems}$, where the set of equations of motion is only integrable. b) {\it Completely integrable systems}, where the set of equations of motion and the action function is integrable. Two examples are studied.

hep-th↗
arXiv2001

Canonical quantization of systems with time-dependent constraints

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase-space coordinates with out using any gauge fixing condition. As a result of the quantization, we obtain the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method.

math-ph↗
arXiv2001

The Hamilton-Jacobi treatment for an abelian Chern-Simons system

The abelian Chern-Simons system is treated as a constrained system using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many variables. It is shown that their simultaneous solutions with the constraints lead to obtain canonical phase space coordinates and the reduced phase space Hamiltonian with out introducing Lagrange multipliers and with out any additional gauge fixing condition.

math-ph↗
arXiv2001

Rdeduced phase-space quantization of constrained systems

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the canonical reduced phase-space coordinates with out using any gauge fixing conditions. The operator and the path integral quantization of these systems is discussed.

math-ph↗
arXiv2000

Path integral quantization of Yang-Mills theory

Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's and Popov's method is not necessary if the canonical path integral formulation is used.

math-ph↗
arXiv2000

On the time evolution in totally constrained systems with weakly vanishing Hamiltonian

The Dirac method treatment for finite dimensional singular systems with weakly vanishing Hamiltonian leads to obtain the equations of motion in terms of parameter $τ$. To obtain the correct equations of motion one should use gauge fixing of the form $τ- f(t)=0$. It is shown that the canonical method leads to describe the evolution in both standard and constrained finite dimensional systems with weakly vanishing Hamiltonian in terms of the physical time $t$, without using any gauge fixing conditions. Besides the operator quantization of the these systems is investigated using the canonical method and it is shown that the evolution of the state $Ψ$ with the time $t$ is described by the Schr/"odinger equation $i\frac{\partial Ψ}{\Partial t} = {\hat H}Ψ$. The extension of this treatment to infinite dimensional systems is given.

math-ph↗
arXiv2000

Canonical path integral quantization of the finite dimensional systems with constraints

The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space coordinates. The path integral is obtained as an integration over the canonical phase space coordinates. This approach is applied to obtain the path integral for three singular systems and it is shown that in our formulation there is no need to distinguish between first and second-class constraints, no need for fixing any gauge, as will as no need to enlarge the phase space.

math-ph↗