Relativistic Symmetries of Bosonic Particles and Antiparticles in the Background of the Position-Dependent Mass for the Improved Deformed Hulthen Plus Deformed Type-Hyperbolic Potential in 3D-EQM Symmetries
Abstract
The bound state solutions of the deformed Klien-Gordon equation have been determined in the three-dimensional extended relativistic quantum mechanics 3D-ERQM symmetries using position-dependent mass (PDM) with unequal scalar and vector potential for the improved Hulthén plus improved deformed type-hyperbolic potential (PDM-SVID(H-TP)) models. PDM with unequal scalar and vector potential for the Hulthén plus deformed type-hyperbolic potential (PDM-(SVH-DTP)) models, as well as a combination of radial terms, which are coupled with the coupling LΘ, which explains the interaction of the physical features of the system with the topological deformations of space-space. The new relativistic energy eigenvalues have been derived using the parametric Bopp shift method and standard perturbation theory which is sensitive to the atomic quantum numbers (j,l,s,m), mixed potential depths (V0S0V1S1), the rest, and perturbed mass (m0,m1), the screening parameter's inverse α, and noncommutativity parameters (Θ,τ,χ). Within the framework of 3D-ERQM symmetries, we have treated certain significant particular instances that we hope will be valuable to the specialized researcher. We have also treated the nonrelativistic limit and applied our obtained results to generate the mass spectra of heavy-light mesons (HLM) such as cc- and bb- under PDM-SE with improved deformed Hulthén plus improved hyperbolic potential (PDM‑ID(H-TP)) models. When the three simultaneous limits (Θ,τ,χ) were applied, we recovered the normal results of relativistic in the literature ( 0,0,0) for the PDM‑ID(H-TP)) models.
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C.A. Onate, A.N. Ikot, M.C. Onyeaju, and M. E. Udoh, “Bound state solutions of D-dimensional Kleine-Gordon equation with hyperbolic potential”, Karbala International Journal of Modern Science, 3(1), 1 (2017). https://doi.org/10.1016/j.kijoms.2016.12.001
U. S. Okorie, A. N. Ikot, C.O. Edet, I.O. Akpan, R. Sever, and R. Rampho, “Solutions of the Klein Gordon equation with generalized hyperbolic potential in D-dimensions”, Journal of Physics Communications, 3, 095015 (2019). https://doi.org/10.1088/2399-6528/ab42c6
H. Hassanabadi, S. Zarrinkamar, and H. Rahimov, “Approximate Solution of D-Dimensional Klein—Gordon Equation with Hulthén-Type Potential via SUSYQM”, Commu. Theor. Phys. 56(3), 423 (2011). https://doi.org/10.1088/0253-6102/56/3/05
U.P., bogo, O.E., Ubi, C.O., Edet, and A. N., Ikot, “Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential”, Eclética Química, 46(4), 60 (2021). https://doi.org/10.26850/1678-4618eqj.v46.4. 2021.p60-73
I.B. Okon, O. Popoola, C.N. Isonguyo, and A.D. Antia, “Solutions of Schrödinger and Klein-Gordon Equations with Hulthen Plus Inversely Quadratic Exponential Mie-Type Potential”, Physical Science International Journal, 19(2), 1 (2018). https://doi.org/10.9734/PSIJ/2018/43610
A.N. Ikot, H.P. Obong, T.M. Abbey, and S. Zare, “Bound and Scattering State of Position Dependent Mass Klein–Gordon Equation with Hulthen Plus Deformed-Type Hyperbolic Potential”, Few-Body Systems, 57(9), 807 (2016). https://doi.org/10.1007/s00601-016-1111-3
L. Canderle, and A. Plastino, “De la Pe na approach for Position-dependent Masses”, Sop transactions on theoretical physics, 1(3), 99 (2014). https://doi.org /10.15764/TPHY.2014.03007
A. Tas, O. Aydogdu, and M. Salti, “Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism”, Annals of Physics, 379, 67 2017). https://doi.org/10.1016/j.aop.2017.02.010
G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, (Les Editions de Physique Halsted Press, France, 1988).
F. Arias de Saavedra, J. Boronat, A. Polls, and A. Fabrocini, “Effective mass of one 4He atom in liquid 3He”, Phys. Rev. B, 50(6) 4248 (1994). https://doi.org/10.1103/PhysRevB.50.4248
M. Barranco, M. Pi, S.M. Gatica, E.S. Hernández, and J. Navarro, “Structure and energetics of mixed 4He-3He drops”, Phys. Rev. B, 56(14), 8997 (1997). https://doi.org/10.1103/PhysRevB.56.8997
P. Ring, and P. Schuck, The Nuclear Many-Body Problem”, (Springer-Verlag, New York, 1980), pp. 211.
L. Dekar, L. Chetouani, and T.F. Hammann, “An exactly soluble Schrödinger equation with smooth position-dependent mass”, J. Math. Phys., 39 (5), 2551 (1998). https://doi.org/10.1063/1.532407
E. Witten, Non-commutative geometry and string field theory”, Nucl. Phys. B, 268, 253 (1986). https://doi.org/10.1016/0550-3213(86)90155-0
S. Doplicher, K., Fredenhagen, and J.E., Spacetime quantization induced by classical gravity, Roberts, Phys. Lett. B, 331(1-2), 39 (1994). https://doi.org/10.1016/0370-2693(94)90940-7
E. Witten, “Reflections on the Fate of Spacetime, Phys. Today, 49(4), 24 (1996). https://doi.org/10.1063/1.881493
A. Kempf, G. Mangano, and R.B. Mann, “Hilbert space representation of the minimal length uncertainty relation”, Physical Review D, 52(2), 1108 (1995). https://doi.org/10.1103/physrevd.52.1108
R.J. Adler, and D.I. Santiago, On gravity and the uncertainty principal”, Modern Physics Letters A, 14(20), 1371 (1999). https://doi.org/10.1142/s0217732399001462
T., Kanazawa, G., Lambiase, G., Vilasi, and A. Yoshioka, Noncommutative Schwarzschild geometry and generalized uncertainty principle”, Eur. Phys. J. C, 79, 95 (2019). https://doi.org/10.1140/epjc/s10052-019-6610-1
F., Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment”, Phys. Lett. B, 452(1-2), 39 (1999). https://doi.org/10.1016/S0370-2693(99)00167-7
A. Maireche, “A New Approach to the Approximate Analytic Solution of the Three-Dimensional Schrӧdinger Equation for Hydrogenic and Neutral Atoms in the Generalized Hellmann Potential Model”, Ukr. J. Phys. 65(11), 987 (2020). https://doi.org/10.15407/ujpe65.11.987
H.S., Snyder, “Quantiz'ed Syace-Time”, Phys. Rev. 71, 38 (1947). https://doi.org/10.1103/PhysRev.71.38
A., Connes, and J., Lott, “Particle models and noncommutative geometry. Nuclear Physics B - Proceedings Supplements, 18(2), 29 (1991). https://doi.org/10.1016/0920-5632(91)90120-4
A. Connes, Noncommutative Geometry, (Academic Press, 1994).
N. Seiberg, E. Witten, N. Seiberg, and E. Witten, String theory and noncommutative geometry. Journal of High Energy Physics, 1999(09), 032 (1999). https://doi.org/10.1088/1126-6708/1999/09/032
A. Maireche, “A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in relativistic noncommutative quantum mechanics and nonrelativistic noncommutative quantum mechanics symmetries”, Rev. Mex. Fis. 67(5), 50702 (2021). https://doi.org/10.31349/revmexfis.67.050702
A., Maireche, “Bound-state solutions of the modified Klien-Gordon and Shrodinger for arbitrary noncommutative quantum mechanics”, J. Phys. Stud. 25(1), 1002 (2021). https://doi.org/10.30970/jps.25.1002
S. Aghababaei, and G. Rezaei, “Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space”, Commun. Theor. Phys. 72, 125101 (2020). https://doi.org/10.1088/1572-9494/abb7cc
J.F.G. Santos, “Heat flow and noncommutative quantum mechanics in phase-space”, Journal of Mathematical Physics, 61(12), 122101 (2020). https://doi.org/10.1063/5.001007
H. Benzair, M. Merad, T. Boudjedaa, and A. Makhlouf, “Relativistic Oscillators in a Noncommutative Space: a Path Integral Approach”, Zeitschrift Für Naturforschung A, 67(1-2), 77 (2012). https://doi.org/10.5560/ZNA.2011-0060
B. Mirza, and M. Mohadesi, “The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space”, Commun. Theor. Phys. (Beijing, China), 42, 664 (2004). https://doi.org/10.1088/0253-6102/42/5/664
H. Motavalli, and A.R. Akbarieh, “Klien-Gordon equation for the Coulomb potential in noncommutative space”, Modern Physics Letters A, 25(29), 2523 (2010). https://doi.org/10.1142/S0217732310033529
M.R. Douglas, and N.A. Nekrasov, “Noncommutative field theory”, Reviews of Modern Physics, 73(4), 977 (2001). https://doi.org/10.1103/RevModPhys.73.977
M. Chaichian, A. Demichev, and P. Prešnajder, “Quantum field theory on non-commutative space-times and the persistence of ultraviolet divergences”, Nuclear Physics B, 567(1-2), 360 (2000). https://doi.org/10.1016/S0550-3213(99)00664-1
L. Mezincescu, “Star Operation in Quantum Mechanics”, (2000). https://arxiv.org/abs/hep-th/0007046
L. Gouba, “A comparative review of four formulations of noncommutative quantum mechanics”, Int. J. Mod. Phys. A, 31(19), 1630025 (2016). https://doi.org/10.1142/s0217751x16300258
F. Bopp, “La mécanique quantique est-elle une mécanique statistique classique particulière”, Ann. Inst. Henri Poincaré, 15(2), 81 (1956). http://www.numdam.org/item/AIHP_1956__15_2_81_0.pdf
A. Maireche, “The investigation of approximate solutions of Deformed Klein-Fock-Gordon and Schrödinger Equations under Modified Equal Scalar and Vector Manning-Rosen and Yukawa Potentials by using the Improved Approximation of the Centrifugal term and Bopp’s shift Method in NCQM Symmetries”, Lat. Am. J. Phys. Educ. 15(2), 2310 (2021). https://dialnet.unirioja.es/descarga/articulo/8128006.pdf
A. Maireche, “A Theoretical Model of Deformed Klein-Gordon Equation with Generalized Modified Screened Coulomb Plus Inversely Quadratic Yukawa Potential in RNCQM Symmetries”, Few-Body Syst. 62, 12 (2021). https://doi.org/10.1007/s00601-021-01596-2
A. Maireche, “Modified unequal mixture scalar vector Hulthén-Yukawa potentials model as a quark-antiquark interaction and neutral atoms via relativistic treatment using the improved approximation of the centrifugal term and Bopp's shift method”, Few-Body Syst. 61, 30 (2020). https://doi.org/10.1007/s00601-020-01559-z
A. Maireche, “The Klein-Gordon equation with modified Coulomb plus inverse-square potential in the noncommutative three-dimensional space”, Mod. Phys. Lett. A, 35(5), 052050015 (2020). https://doi.org/10.1142/s0217732320500157
A. Maireche, “Heavy quarkonium systems for the deformed unequal scalar and vector Coulomb-Hulthén potential within the deformed effective mass Klein-Gordon equation using the improved approximation of the centrifugal term and Bopp's shift method in RNCQM symmetries”, Int. J. Geo. Met. Mod. Phys. 18(13), 2150214 (2021). https://doi.org/10.1142/S0219887821502145
A. Maireche, “A new theoretical study of the deformed unequal scalar and vector Hellmann plus modified Kratzer potentials within the deformed Klein-Gordon equation in RNCQM symmetries”, Mod. Phys. Lett. A, 36(33), 2150232 (2021). https://doi.org/10.1142/S0217732321502321
A. Maireche, “On the interaction of an improved Schiöberg potential within the Yukawa tensor interaction under the background of deformed Dirac and Schrödinger equations”, Indian J Phys, 96(10), (2022). https://doi.org/10.1007/s12648-022-02433-w
A. Maireche, “Approximate Arbitrary (k,l) states solutions of deformed Dirac and Schrodinger equations with new generalized Schioberg and Manning-Rosen Potentials within the generalized tensor Interactions in 3D-EQM Symmetries”, Int. J. Geo. Met. Mod. Phys. (2022). https://doi.org/10.1142/S0219887823500287
A. Kurniawan, A. Suparmi, and C. Cari, “Approximate analytical solution of the Dirac equation withq-deformed hyperbolic Pöschl–Teller potential and trigonometric Scarf II non-central potential”, Chinese Physics B, 24(3), 030302 (2015). https://doi.org/10.1088/1674-1056/24/3/030302
A.N. Ikot, H.P. Obong, T.M. Abbey, S. Zare, M. Ghafourian, and H. Hassanabadi, “Bound and Scattering State of Position Dependent Mass Klein–Gordon Equation with Hulthen Plus Deformed-Type Hyperbolic Potential”, Few-Body Syst. 57, 807 (2016). https://doi.org/10.1007/s00601-016-1111-3
S.H. Dong, W.C. Qiang, G.H. Sun, and V.B. Bezerra, “Analytical approximations to the l-wave solutions of the Schrödinger equation with the Eckart potential”, J. Phys. A: Math. Theor. 40(34), 10535 (2007). https://doi.org/10.1088/1751-8113/40/34/010
Y. Zhang, “Approximate analytical solutions of the Klein-Gordon equation with scalar and vector Eckart potentials”, Phys. Scr. 78(1), 015006-1 (2008). https://doi.org/10.1088/0031-8949/78/01/015006
K. Bencheikh, S. Medjedel, and G. Vignale, “Current reversals in rapidly rotating ultracold Fermi gases”, Phys. Lett. A, 89(6), 063620-1-(2014). https://doi.org/10.1103/physreva.89.063620
W. Gao-Feng, C. Wen-Li, W. Hong-Ying, and L. Yuan-Yuan, “The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term”, Chinese Physics B, 18(9), 3663 (2009). https://doi.org/10.1088/1674-1056/18/9/010
R.D. Woods, and D.S. Saxon, “Diffuse Surface Optical Model for Nucleon-Nuclei Scattering”, Physical Review, 95(2), 577 (1954). https://doi.org/10.1103/physrev.95.577
M. Abu-Shady, T.A. Abdel-Karim, and S.Y. Ezz-Alarab, “Masses and thermodynamic properties of heavy mesons in the non-relativistic quark model using the Nikiforov–Uvarov method”, J. Egypt Math. Soc. 27, 14 (2019). https://doi.org/10.1186/s42787-019-0014-0
R. Rani, S.B. Bhardwaj, and F. Chand, “Mass Spectra of Heavy and Light Mesons Using Asymptotic Iteration Method”, Communications in Theoretical Physics, 70(2), 179 (2018). https://doi.org/10.1088/0253-6102/70/2/179
A. Maireche, “Analytical Expressions to Energy Eigenvalues of the Hydrogenic Atoms and the Heavy Light Mesons in the Framework of 3D-NCPS Symmetries Using the Generalized Bopp's Shift Method”, Bulg. J. Phys. 49(3), 239 (2022). https://doi.org/10.55318/bgjp.2022.49.3.239
A. Maireche, “The investigation of approximate solutions of Deformed Schrödinger Equations for the Hydrogenic Atoms, Heavy Quarkonium Systems ( = , ) and Diatomic molecule Bound-State Problem under Improved Exponential, Generalized, Anharmonic Cornell potential Model in NCPS symmetries”, Lat. Am. J. Phys. Educ. 16(2), 2304-1 ( 2022). https://dialnet.unirioja.es/descarga/articulo/8602824.pdf
A., Maireche, “ The Relativistic and Nonrelativistic Solutions for the Modified Unequal Mixture of Scalar and Time-Like Vector Cornell Potentials in the Symmetries of Noncommutative Quantum Mechanics”, Jordan Journal of Physics, 14(1), 59 (2021). https://doi.org/10.47011/14.1.6
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