Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

Lütfüoğlu, B. C.; Lipovský, Jiř̌í; Křı́ž, Jan

doi:10.1140/epjp/i2018-11852-0

Cited by 17 publications

(23 citation statements)

References 58 publications

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“…2. One of the authors of this study, BCL, in a study published in 2018, examined the generalized symmetric Woods-Saxon potential energy with a constant mass term in the KG equation and showed that an energy spectrum at the EMOS limit cannot be obtained [42]. The results obtained in this study are in agreement with the results given by BCL.…”

Section: Resultssupporting

confidence: 85%

“…Among a large number of articles, we would like to underline the investigations that employ Woods-Saxon [6], Hulthén [7], Morse [8], Rosen-Morse [9] , Eckart [10], Manning-Rosen [11], Pöschl-Teller [12], Kratzer [13], Hylleraas [14], multiparameter [15], exponential-type molecule [16], pseudoharmonic oscillator [17], Hartmann [18], double ring-shaped oscillator [19] potential energies.…”

Section: Introductionmentioning

confidence: 99%

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Bound state solutions of the Klein Gordon equation with energy-dependent potentials

Lütfüoğlu,

Ikot,

Karakoc

et al. 2019

Preprint

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In this manuscript, we investigate the exact bound state solution of the Klein Gordon equation with an energy-dependent Coulomb-like potential energy in the presence of position-energy dependent mass. First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign. Then, we extend the investigation with the cases where the mixed potential energies have equal magnitude and opposite sign. Furthermore, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a non-trivial relation between the tuning parameters which lead the examined problem to a constant mass one. Finally, we employ the Secant method to calculate the energy spectra. We use the calculated spectra and show that the unnormalized wave functions satisfy the boundary conditions. We conclude the manuscript with a comparison of the calculated energy spectra versus tuning parameters.

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Section: Resultssupporting

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Bound state solutions of the Klein Gordon equation with energy-dependent potentials

Lütfüoğlu,

Ikot,

Karakoc

et al. 2019

Preprint

Self Cite

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“…In this section, we consider the Coulomb potential V (r) = − Ze 2 r and intend to derive a solution in three dimensional Dunkl-Klein-Gordon equation. We start by expressing the stationary Dunkl-Klein-Gordon equation according to [36]…”

Section: Coulomb Potentialmentioning

confidence: 99%

Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential

Hamil¹,

Lütfüoğlu²

2021

Preprint

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Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate solutions for two important problems in three-dimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the Dunkl-Klein-Gordon oscillator solutions with the Cartesian and spherical coordinates. In both coordinate systems, we find that the differential equations are separable and their eigenfunctions can be given in terms of the associate Laguerre and Jacobi polynomials. We observe how the Dunkl formalism is affecting the eigenvalues as well as the eigenfunctions. As a second problem, we examine the Dunkl-Klein-Gordon equation with the Coulomb potential. We obtain the eigenvalue, their corresponding eigenfunctions, and the Dunkl-fine structure terms.

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“…The Nikiforov-Uvarov method [8], factorization method [9], Laplace transform approach [10], and the path integral method [11] and shifted 1/N expansion approach [12,13] are used for solving radial and azimuthal parts of the wave equations exactly or quasiexactly in l ≠ 0 for various potentials. Additionally, there are numerous interesting research works about the KFG equation with physical potentials by using different methods in the literature [14][15][16][17][18][19][20][21][22][23][24][25][26]. Among them, as an example, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Ahmadov

Aslanova

Orujova

et al. 2021

Advances in High Energy Physics

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The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary l states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

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Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

Cited by 17 publications

References 58 publications

Bound state solutions of the Klein Gordon equation with energy-dependent potentials

Bound state solutions of the Klein Gordon equation with energy-dependent potentials

Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential

Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

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