Extension of perturbation theory to quantum systems with conformable derivative

Al-Masaeed, Mohamed.; Rabei, Eqab M.; Al-Jamel, Ahmed; Băleanu, Dumitru

doi:10.1142/s021773232150228x

Cited by 7 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, power series expansions and Laplace transform techniques were extended to the conformable derivative framework [2]. The conformable derivative has found widespread use in various disciplines, with a particular emphasis on applied sciences [3][4][5] and physics [6][7][8]. Its application has proven to be valuable in solving problems and addressing phenomena in these fields.…”

Section: Introductionmentioning

confidence: 99%

On the Geometric and Physical Properties of Conformable Derivative

Has,

Yılmaz,

Baleanu

2024

Mathematical Sciences and Applications E-Notes

Self Cite

View full text Add to dashboard Cite

In this article, we explore the advantages and geometric and physically implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. To enhance comprehension and visualize the concepts discussed, the article presents several examples. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physically implications of the conformable derivative.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Geometric and Physical Properties of Conformable Derivative

Has,

Yılmaz,

Baleanu

2024

Mathematical Sciences and Applications E-Notes

Self Cite

View full text Add to dashboard Cite

show abstract

“…The fractional Christ-Lee model is then discussed and quantized using WKB approximation to demonstrate the applicability of their work. Using conformable calculus, the approximation methods employed in quantum mechanics have recently been extended to become usable in conformable quantum mechanics (Variational method [29] , Perturbation theory [30] and WKB approximation [31] ). In addition the conformable harmonic oscillator is quantized by using α -creation and α -annihilation operators [32].…”

Section: Introductionmentioning

confidence: 99%

Quantization of the Bateman damping system with conformable derivative

AlBanwa¹,

Al-Jamel²,

Rabei³

et al. 2023

Preprint

View full text Add to dashboard Cite

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 ≤ 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 α n and eigenfunctions ψ α n 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.

show abstract

“…[25] introduced Riemannian geometry through using the conformable fractional derivative in Christoffel index symbols of the first and second kind. The conformable calculus has been used in making an extension of approxima-tion methods to become applicable to conformable quantum mechanics [26][27][28], and to find solutions of related differential equations such as the conformable Laguerre and associated Laguerre equations [29]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

The effect of deformation of special relativity by conformable derivative

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are 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, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

show abstract

Extension of perturbation theory to quantum systems with conformable derivative

Cited by 7 publications

References 29 publications

On the Geometric and Physical Properties of Conformable Derivative

On the Geometric and Physical Properties of Conformable Derivative

Quantization of the Bateman damping system with conformable derivative

The effect of deformation of special relativity by conformable derivative

Contact Info

Product

Resources

About