The influence of noncommutativity on the energy spectra of bosonic particles in the framework of the DKGE with improved spatially-dependent mass including mixed scalar-vector Coulomb potentials in the ERQM symmetries
DOI:
https://doi.org/10.31349/RevMexFis.69.030801Keywords:
Klien-Gordon equation, spatially-dependent mass, mixed scalar-vector Coulomb potentials, Noncommutative Quantum mechanics, Star productAbstract
The bound state solutions of the deformed Klien-Gordon equation (DKGE) have been determined in the extended relativistic quantum mechanics ERQM symmetries using the improved spatially-dependent mass Coulomb potential with mixed scalar-vector Coulomb potentials (ISDM-SVCPs) model. The spatially-dependent mass Coulomb potential, as well as a combination of ((1/(r³)) and (1/(r⁴))), are included in the ISDM-SVCPs model, which is coupled with the coupling LΘ, which explains the interaction of the physical features of the system with the topological deformations of space-time. The new relativistic energy eigenvalues for the ISDM-CP have been derived using the parametric Bopp's shift method and standard perturbation theory. Quantum numbers (j,l,s,m), mixed potential depths (q/s_{c},m₀,m₁), and noncommutativity parameters (Θ,τ,χ) seemed to affect the new values we obtained. Within the framework of relativistic extended quantum mechanics, we have addressed certain significant particular instances that we hope will be valuable to the specialized researcher. In DKGE symmetries, we've also looked at the improved pure scalar Coulomb-like potential. The formulation of total energy was also discovered in the context of extended symmetries, which unified the energies of bosonic particles and antiparticles into a single mathematical formula. When the three simultaneous limits (Θ,τ,χ) were applied, we recovered the normal results of relativistic in the literature (0,0,0).
References
: K. Bakke, and C. Furtado, On the Klein-Gordon oscillator subject to a Coulomb-type potential, Annals of Physics 355 (2015) 48, https://doi.org/10.1016/j.aop.2015.01.028
: R.L.L. Vitória, C. Furtado, and K. Bakke, On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein-Gordon oscillator and the Coulomb potential, Annals of Physics 370 (2016) 128, https://doi.org/10.1016/j.aop.2016.03.016
: A. De Souza Dutra, and C.S. Jia, Classes of exact Klein--Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential, Phys. Lett. A 352(6) (2006) 484, https://doi.org/10.1016/j.physleta.2005.12.0
: H. Motavalli, and A.R. Akbarieh, Klien-Gordon equation for Coulomb potential in noncommutative space, Mod. Phys. Lett. A 25(29) (2010) 2523, https://doi.org/10.1142/s0217732310033529
: M. Darroodi, H. Mehraban, and S. Hassanabadi, The Klein--Gordon equation with the Kratzer potential in the noncommutative space, Mod. Phys. Lett. A 33 No. 35 (2018) 1850203, https://doi.org/10.1142/s0217732318502036
: 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) (2020) 052050015, 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) (2021) 2150214, https://doi.org/10.1142/S0219887821502145
: 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 J. Phys. 14 (1), (2021) 59, https://doi.org/10.47011/14.1.6
: 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 (2021) 12, https://doi.org/10.1007/s00601-021-01596-2
: A. Maireche, The Investigation of Approximate Solutions of Deformed Klein-Gordon and Schrödinger Equations Under Modified More General Exponential Screened Coulomb Potential Plus Yukawa Potential in NCQM Symmetries, Few-Body Syst 62 (2021) 66, https://doi.org/10.1007/s00601-021-01639-8
: A. Maireche, Heavy light mesons in the symmetries of extended nonrelativistic quark model, Yanbu J. Eng. Sc. 17 (2019) 51, https://doi.org/10.53370/001c.23732
: A. Maireche, A new study of energy levels of hydrogenic atoms and some molecules for new more general exponential screened Coulomb potential, Open Acc J Math Theor Phy. 1(6) (2018) 232, https://doi.org/10.15406/oajmtp.2018.01.00040
: A. Maireche, A theoretical investigation of nonrelativistic bound state solution at finite temperature using the sum of modified Cornell plus inverse quadratic potential, Sri Lankan J. of Phys. 21(2020) 11, http://doi.org/10.4038/sljp.v21i1.8069
: A. Maireche, New Relativistic Atomic Mass Spectra of Quark (u, d and s) for Extended Modified Cornell Potential in Nano and Plank's Scales, J. Nano- Electron. Phys. 8 (1) (2016) 01020, https://doi.org/ 10.21272/jnep.8(1).01020
: X.Y. Gu, Z.Q. Ma and, S.H. Dong, Exact -solutions to the Dirac equation for a Coulomb potential in D+1 dimensions, Int. J. Mod. Phys. E 11(04) (2002) 335, https://doi.org/10.1142/s0218301302000879
: S.H. Dong, The Dirac equation with a Coulomb potential in D dimensions, J. Phys. A: Math. Gen. 36 (2003) 4977, https://doi.org/10.1088/0305-4470/36/18/303
: Z.Q. Ma, S.H. Dong, X.Y. Gu, J. Yu and, M. Lozada-cassou, The Klien-Gordon equation with a Coulomb plus scalar potential in D dimensions, Int. J. Mod. Phys. E 13(03) (2004) 597, https://doi.org/10.1142/s0218301304002338
: S. H. Dong, X. Y. Gu, Z.Q. Ma and, J. Yu, The Klein--Gordon Equation with a Coulomb Potential in D Dimensions, Int. J. Mod. Phys. E 12(04) (2003) 555, https://doi.org/10.1142/s0218301303001387
: M. Hamzavi, A.A. Rajabi and, H. Hassanabadi, Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method, Phys. Lett. A 374(42) (2010) 4303, https://doi.org/10.1016/j.physleta.2010.08.065
: S.M. Ikhdair and, R. Sever, Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential, Applied Mathematics and Computation 216(2) (2010) 545, https://doi.org/10.1016/j.amc.2010.01.072
: S. M. Ikhdair, Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials, Eur. Phys. J. A 40(2) (2009) 143, https://doi.org/10.1140/epja/i2009-10758-9
: T.C. Adorno, M.C. Baldiotti, M. Chaichian, D.M. Gitman and, A. Tureanu, Dirac equation in noncommutative space for hydrogen atom, Phys. Lett. B 682(2) (2009) 235, https://doi.org/10.1016/j.physletb.2009.11.003
: V.G. Kupriyanov, A hydrogen atom on curved noncommutative space, J. Phys. A: Math. Theor. 46 (2013) 245303, https://doi.org/10.1088/1751-8113/46/24/245303
: N. Chair and, M.A. Dalabeeh, The noncommutative quadratic Stark effect for the H-atom, J. Phys. A: Math. Gen. 38(7) (2005) 1553, https://doi.org/10.1088/0305-4470/38/7/010
: M. Chaichian, M.M. Sheikh-Jabbari and, A. Tureanu, Non-commutativity of space-time and the hydrogen atom spectrum, Eur. Phys. J. C 36(2) (2004) 251, https://doi.org/10.1140/epjc/s2004-01886-1
: M. Chaichian, M.M. Sheikh-Jabbari, and A. Tureanu, Hydrogen atom spectrum and the Lamb Shift in noncommutative QED, Phys. Rev. Lett. 86(13) (2001) 2716, https://doi.org/10.1103/physrevlett.86.2716.
: M. Solimanian, J. Najia, and Kh. Ghasemian, The noncommutative parameter for cc in nonrelativistic limit, Eur. Phys. J. Plus 137:331 (2022), https://doi.org/10.1140/epjp/s13360-022-02546-5
: O. Bertolami, J.G. Rosa, C.M.L. De Aragao, P. Castorina, and D. Zappala, Scaling of variables and the relation between noncommutative parameters in noncommutative quantum mechanics, Mod. Phys. Lett. A 21(10) (2006) 795, https://doi.org/10.1142/s0217732306019840
: A. Mirjalili, and M. Taki, Noncommutative correction to the Cornell potential in heavy-quarkonium atoms, Theor. Math. Phys. 186(2) (2016) 280, https://doi.org/10.1134/s0040577916020112
: A. Connes, M.R. Douglas, and A. Schwarz, Noncommutative geometry and Matrix theory, JHEP 02 (1998) 003, https://doi.org/10.1088/1126-6708/1998/02/003
: S. Capozziello, G. Lambiase, and G. Scarpetta, Generalized uncertainty principle from quantum geometry, Int. J. Theor. Phys. 39 (2000) 15, https://doi.org/10.1023/A:1003634814685
: S. Doplicher, K. Fredenhagen, and J.E. Roberts, Spacetime quantization induced by classical gravity, Phys. Lett. B 331(1-2) (1994) 39, https://doi.org/10.1016/0370-2693(94)90940-7
: E. Witten, Refection on the fate spacetime, Phys. Today 49(4) (1996) 24, https://doi.org/10.1063/1.881493
: A. Kempf, G. Mangano, and R.B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52(2) (1995) 1108, https://doi.org/10.1103/physrevd.52.1108
: R.J. Adler, and D.I. Santigo, On gravity and the uncertainty principal, Mod. Phys. Lett. A 14 (20) (1999) 1371, 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(2) (2019) 95, 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) (1999) 39, https://doi.org/10.1016/s0370-2693(99)00167-7
: H.S. Snyder, Quantized Space-Time, Phys. Rev. 71 (1947) 38, https://doi.org/10.1103/PhysRev.71.38; The Electromagnetic Field in Quantized Space-Time. 72 (1947) 68, https://doi.org/10.1103/PhysRev.72.68
: A. Connes, Noncommutative Geometry (ISBN-9780121858605) (1994).
: A. Connes, and J. Lott, Particle models and noncommutative geometry (expanded version), Nucl. Phys. Proc. Suppl. 18B (1991) 29.
: N. Seiberg, and E. Witten, String theory and noncommutative geometry, JHEP 1999(09) (1999) 32, https://doi.org/10.1088/1126-6708/1999/09/032
: P. Nicolini, Noncommutative black holes, the final appeal to quantum gravity: a review, Int. J Mod. Phys. A 24(07) (2009) 1229, https://doi.org/10.1142/s0217751x09043353
: A. Maireche, A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry, Int. Front. Sci. Lett. 10 (2016) 8, https://doi.org/10.18052/www.scipress.com/IFSL.10.8
: A. Maireche, New Relativistic Bound States for Modified Pseudoharmonic Potential of Dirac Equation with Spin and Pseudo-Spin Symmetry in One-electron Atoms, Afr. Rev. Phys.12: 0018 (2017) 130.
: K.P. Gnatenko, Kinematic variables in noncommutative phase space and parameters of noncommutativity, Mod. Phys. Lett. A 32(31) (2017) 1750166 (12 pages) , https://doi.org/10.1142/s0217732317501668
: A. Maireche, New bound-state solutions of the deformed Klien-Gordon and Shrodinger equations for arbitrary l-state with the modified equal vector and scalar Manning-Rosen plus a class of Yukawa potentials in RNCQM and NRNCQM symmetries, J. Phys. Stud. 25(4) (2021) 4301, https://doi.org/10.30970/jps.25.4301
: A. Maireche, Nonrelativistic Atomic Spectrum for Companied Harmonic Oscillator Potential and its Inverse in both NC-2D: RSP, Int. Lett. Chem. Phys. Astr. 56 (2015) 1, https://doi.org/10.18052/www.scipress.com/ILCPA.56.1
: P.M. Ho, and H.C. Kao, Noncommutative quantum mechanics from noncommutative quantum field Theory, Phys. Rev. Lett. 88(15) (2002 ) 151602-1, https://doi.org/10.1103/physrevlett.88.151602
: K.P. Gnatenko, Composite system in noncommutative space and the equivalence principle, Phys. Lett. A 377(43) (2013) 3061, https://doi.org/10.1016/j.physleta.2013.09.036
: 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.
: E.F. Djemaï, and H. Smail, On quantum mechanics on noncommutative quantum phase space, Commun. Theor. Phys. 41(6) (2004) 837, https://doi.org/10.1088/0253-6102/41/6/837
: A. Maireche, Bound state solutions of Klein-Gordon and Schrödinger equations with linear combination of Hulthén and Kratzer potentials, Afr. Rev Phys. 15:003 (2020) 19.
: O. Bertolami, J. G. Rosa, C.M. L. de Aragão, P. Castorina, and D. Zappalà, Noncommutative gravitational quantum well, Phys. Rev. D 72(2) (2005) 025010-1, https://doi.org/10.1103/physrevd.72.025010
: S. I. Vacaru, Exact solutions with noncommutative symmetries in Einstein and gauge gravity, J. Math. Phys. 46(4) (2005) 042503, https://doi.org/10.1063/1.1869538
: A. Maireche, A New Approach to the approximate analytic solution of the three-dimensional Schrödinger equation for Hydrogenic and neutral atoms in the generalized Hellmann potential model, Ukr. J. Phys. 65(11) (2020) 987, https://doi.org/10.15407/ujpe65.11.987
: J. Zhang, Fractional angular momentum in non-commutative spaces, Phys. Lett. B 584(1-2)(2004) 204, https://doi.org/10.1016/j.physletb.2004.01.049
: A. Maireche, A new Theoretical Investigations of the Modified Equal Scalar and Vector Manning-Rosen plus quadratic Yukawa Potential within the Deformed Klein-Gordon and Schrodinger Equations using the Improved Approximation of the Centrifugal term and Bopp's shift Method in RNCQM and NRNCQM Symmetries, SPIN J. 11, No. 04 (2021) 2150029, https://doi.org/10.1142/S2010324721500296
: 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, No. 2 (2021) 2310-1.
: A. Maireche, Bound-state solutions of the modified Klein-Gordon and Schrödinger equations for arbitrary l-state with the modified Morse potential in the symmetries of noncommutative quantum mechanics, J. Phys. Stud. 25(1) (2021) 1002. https://doi.org/10.30970/jps.25.1002
: A. Maireche, Nonrelativistic treatment of Hydrogen-like and neutral atoms subjected to the generalized perturbed Yukawa potential with centrifugal barrier in the symmetries of noncommutative Quantum mechanics, Int. J. Geo. Met. Mod. Phys. 17(5) (2020) 2050067, https://doi.org/10.1142/S021988782050067X
: S. Aghababaei, and G. Rezaei, Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space. Commun. Theor. Phys. 72 (2020) 125101, https://doi.org/10.1088/1572-9494/abb7cc
: J. Wang, and K. Li, The HMW effect in noncommutative quantum mechanics, J. Phys. A Math. Theor. 40(9) (2007) 2197, https://doi.org/10.1088/1751-8113/40/9/021
: A. Maireche, A theoretical study of the modified equal scalar and vector Manning-Rosen potential within the deformed Klein-Gordon and Schrödinger in RNCQM and NRNCQM symmetries, Rev. Mex. Fis. 67(5) (2021) 050702, https://doi.org/10.31349/RevMexFis.67.050702
: E. M.C. Abreu, J.A. Neto, A.C.R. Mendes C. Neves, W. Oliveira, and M.V. Marcial, Lagrangian formulation for noncommutative nonlinear systems, Int. J. Mod. Phys. A 27 (2012) 1250053, https://doi.org/10.1142/s0217751x12500534
: A. Maireche, A model of modified Klein-Gordon equation with modified scalar-vector Yukawa potential, Afr. Rev Phys. 15: 0001 (2020) 1.
: A. Maireche, Investigations on the Relativistic Interactions in One-Electron Atoms with Modified Yukawa Potential for Spin 1/2 Particles, Int. Front. Sci. Lett. 11 (2017) 29, https://doi.org/10.18052/www.scipress.com/IFSL.11.29
: Y. Yi, K. Kang, W. Jian-Hua, and C. Chi-Yi, Spin-1/2 relativistic particle in a magnetic field in NC phase space, Chin. Phys. C 34(5) (2010) 543, https://doi.org/10.1088/1674-1137/34/5/005
: A. Maireche, A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential, J. Nano- Electron. Phys. 8 No 4(1) (2016) 04027, https://doi.org/10.21272/jnep.8(4(1)).04027
: 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) (2016) 1630025, https://doi.org/10.1142/s0217751x16300258
: F. Bopp, La mécanique quantique est-elle une mécanique statistique classique particulière, Ann. Inst. Henri Poincaré 15(2) (1956) 81.
: J. Gamboa, M. Loewe, and J.C. Rojas, Noncommutative quantum mechanics, Phys. Rev. D. 64 (2001) 067901, https://doi.org/10.1103/PhysRevD.64.067901.
: A. Maireche, Extended of the Schrödinger Equation with New Coulomb Potentials plus Linear and Harmonic Radial Terms in the Symmetries of Noncommutative Quantum Mechanics, J. Nano- Electron. Phys. 10(6) (2018) 06015-1, https://doi.org/10.21272/jnep.10(6).06015
: A. Maireche, A Recent Study of Excited Energy Levels Diatomics for Modified more General Exponential Screened Coulomb Potential: Extended Quantum Mechanics, J. Nano- Electron. Phys. 9 (3) (2017) 03021, https://doi.org/10.21272/jnep.9(3).03021
: A. Maireche, Solutions of Klein-Gordon equation for the modified central complex potential in the symmetries of noncommutative quantum mechanics, Sri Lankan J. of Phys. 22(1) (2021) 1, http://doi.org/10.4038/sljp.v22i1.8079
: A. Maireche, Theoretical Investigation of the Modified Screened cosine Kratzer potential via Relativistic and Nonrelativistic treatment in the NCQM symmetries, Lat. Am. J. Phys. Educ. 14 (3) (2020) 3310-1.
: H. Motavalli, and A.R. Akbarieh, Klein-Gordon equation for the Coulomb potential in noncommutative space., Mod. Phys. Lett. A 25(29) (2010) 2523, https://doi.org/10.1142/s0217732310033529
: M. Darroodi, H. Mehraban and H. Hassanabadi, The Klein-Gordon equation with the Kratzer potential in the noncommutative space, Mod. Phys. Lett. A 33(35) (2018) 1850203, https://doi.org/10.1142/s0217732318502036
: 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 Vol. 36(33) (2021) 2150232, https://doi.org/10.1142/S0217732321502321
: A. Maireche, Diatomic Molecules with the Improved Deformed Generalized Deng--Fan Potential Plus Deformed Eckart Potential Model through the Solutions of the Modified Klein-Gordon and Schrödinger Equations within NCQM Symmetries,Ukr. J. Phys. 67(3) (2022) 183, https://doi.org/10.15407/ujpe67.3.183
: A. Maireche, New relativistic and nonrelativistic model of diatomic molecules and fermionic particles interacting with improved modified Mobius potential in the framework of noncommutative quantum mechanics symmetries, Yanbu J. Eng. Sc. 18(1) (2021) 10, https://doi.org/10.53370/001c.28090
: A. Maireche, Approximate k-state solutions of the deformed Dirac equation in spatially dependent mass for the improved Eckart potential including the improved Yukawa tensor interaction in ERQM symmetries, Int. J. Geo. Met. Mod. Phys. 19(06) (2022) 2250085, https://doi.org/10.1142/S0219887822500852
: A. Maireche, Diatomic Molecules and Fermionic Particles With Improved Hellmann-Generalized Morse Potential through the Solutions of the Deformed Klein-Gordon, Dirac and Schrödinger Equations in Extended Relativistic Quantum Mechanics and Extended Nonrelativistic Quantum Mechanics Symmetries, Rev. Mex. Fis. 68 (2) (2022) 020801, https://doi.org/10.31349/RevMexFis.68.020801
: A. Maireche, Approximate Arbitrary k State Solutions of Dirac Equation with Improved Inversely Quadratic Yukawa Potential within Improved Coulomb-like Tensor Interaction in Deformation Quantum Mechanics Symmetries,Few-Body Syst. 63, 54 (2022), https://doi.org/10.1007/s00601-022-01755-z
: A. Saidi, and M. B. Sedra, Spin-one (1+3)-dimensional DKP equation with modified Kratzer potential in the non-commutative space. Mod. Phys. Lett. A 35(5) (2020) 2050014, https://doi.org/10.1142/s0217732320500145
: A. Houcine, and B. Abdelmalek, Solutions of the Duffin-Kemmer Equation in Non-Commutative Space of Cosmic String and Magnetic Monopole with Allowance for the Aharonov-Bohm and Coulomb Potentials, Phys. Part. Nuc. Lett. 16 (3) (2019) 195.
: Wolfram Research: https://functions.wolfram.com/
: K. Bencheikh, S. Medjedel and G. Vignale, Current reversals in rapidly rotating ultracold Fermi gases, Phys. Lett. A 89(6) (2014) 063620-1, https://doi.org/10.1103/physreva.89.063620
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