Matrix Continued Fraction Solution to the Relativistic Spin-0 Feshbach–Villars Equations

We propose a solution method for studying relativistic spin-0 particles. We adopt the Feshbach-Villars formalism of the Klein-Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulomb-Sturmian basis. The corresponding Green's operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider Coulomb plus short range vector potential for bound and resonant states and linear confining scalar potentials for bound states. The continued fraction is naturally divergent at resonant state energies, but we made it convergent by an appropriate analytic continuation.

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“…This method has been used in Ref. [9] for calculating bound states. The matrix continued fraction was evaluated iteratively.…”

Section: Coulomb Plus Short Range Potentialmentioning

confidence: 99%

“…In a recent work we have proposed a solution method for the Feshbach-Villars equations [9]. The method amounts to rewriting the eigenvalue problem into an integral equation form and representing the equation on a discrete Hilbert space basis.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Spin-0 Feshbach–Villars Equations for Polynomial Potentials

2019

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“…In recent decades, a number of papers have been produced with the aim of exploring the relativistic dynamical properties of single particles and solving their wave equations by adopting the FV scheme (e.g, Refs. [34][35][36][37][38][39][40] and other related references cited therein).…”

Section: Introductionmentioning

confidence: 98%

Statistical proerties of the two-dimensional Feshbach-illars oscillator (FVO) in the rotating cosmic string

Bouzenada¹,

Boumali²

2023

Preprint

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This paper is concerned with an investigation of the quantum mechanical dynamics of massive, spinless relativistic Klein-Gordon particle in the space-time generated by a rotating cosmic string. The equations of motion are found by the use of the first-order Feshbach-Villars formulation of the Klein-Gordon equation. The wave-functions and the associated energies were deduced ( both in the free and in the interaction case). Following that, the partition function was approximated using Zeta function representation. Moreover, by considering the energy spectrum of the system in question, the thermal properties are presented. We examine the behavior of these properties as a function of the physical parameters of the model such as rotation, curvature, and quantum numbers. Therefore, the impact of the topological defect on the quantum system under investigation is discussed.

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“…In recent years, a significant number of studies have been devoted to exploring the dynamical properties of single particles in a relativistic context and solving their wave equations using the FV approach. For example (see [41][42][43][44][45][46][47]), Bouzenada et al [48] investigated the Feshbach-Villars oscillator (FVO) case in a spinning cosmic string space-time and reported their findings on the thermal properties and density of the system.…”

Section: Introductionmentioning

confidence: 99%