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l-Wave Solutions of Duffin-Kemmer-Petiau Equation in (1 + 3) Dimension in the Presence of Frost-Musulin Potential

Year 2021, Volume: 16 Issue: 2, 444 - 457, 25.11.2021
https://doi.org/10.29233/sdufeffd.934867

Abstract

In this study, the analytical solutions of Duffin-Kemmer-Petiau equation in (1+3) Dimensions for spin-1 particles in the presence of Frost-Musulin potential were obtained. The standard method was used to obtain these solutions and an approach to the centripetal term was applied. Using the equations obtained, the bound state solutions are expressed in terms of Gaussian hypergeometric functions. Using the boundary conditions of wave functions, the equation giving the bound state energy eigenvalues for any l-state is derived. The bound state energy values for any l-state were determined numerically using the Mathematica software package. In addition, the effects of potential parameters on energy eigenvalues were examined graphically and numerically.

References

  • [1] N. Kemmer, “The particle aspect of meson theory,” Proc. of the Roy. Soc. of Lon., 173 (952), 91-116, 1939
  • [2] R. J. Duffin, “On the characteristic matrices of covariant systems,” Phys. Rev., 54 (12), 1114, 1938
  • [3] G. Petiau, “Contribution a la theorie des equations dondes corpusculaire,” Ph.D. Thesis, University of Paris, Published in Acad. Roy. de Belg., Classe Sci., Mem in 8, 16 (2), 1936.
  • [4] R. E. Kozack, B. C. Clark, S. Hama, V. K. Mishra, R. L. Mercer, and L. Ray, “Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering,” Phys. Rev. C, 40 (5), 2181, 1989.
  • [5] V. Gribov, “QCD at large and short distances (annotated version),” EPJC, 10 (1), 71-90, 1999.
  • [6] Y. Nedjadi and R. C. Barrett, “On the properties of the Duffin-Kemmer-Petiau equation,” J. Phys. G, 19 (1), 87, 1993.
  • [7] Y. Nedjadi and R. C. Barrett, “The Duffin-Kemmer-Petiau oscillator,” J. Phys. A, 27 (12), 4301, 1994.
  • [8] Y. Nedjadi and R. C. Barrett, “Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson,” J. Math. Phys., 35 (9), 4517-4533, 1994.
  • [9] H. Hassanabadi, S. F. Forouhandeh, H. Rahimov, S. Zarrinkamar, and B. H. Yazarloo, “Duffin–Kemmer–Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation,” Can. J. Phys., 90 (3), 299-304, 2012.
  • [10] M. Hamzavi and S. M. Ikhdair, “Approximate solution of the Duffin–Kemmer–Petiau equation for a vector Yukawa potential with arbitrary total angular momenta,” FBYS, 54 (11), 1753-1763, 2013.
  • [11] S. Zarrinkamar, A. A. Rajabi, B. H. Yazarloo, and H. Hassanabadi, “An approximate solution of the DKP equation under the Hulthén vector potential,” Chin. Phys. C, 37 (2), 023101, 2013.
  • [12] M. K. Bahar, “AIM solutions to the DKP equation for spin-1 particles in the presence of kratzer potential in (2+1) dimensions,” FBYS, 54 (11), 2133-2142, 2013.
  • [13] M. K. Bahar and F. Yasuk, “Relativistic spin-1 particles with position-dependent mass under the Coulomb interaction: Exact analytical solutions of the DKP equation,” Can. J. Phys., 91 (3), 191-197, 2013.
  • [14] M. K. Bahar and F. Yasuk, “Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential,” Can. J. Phys 92 (12), 1565-1569, 2014.
  • [15] C. A. Onate, J. O. Ojonubah, A. Adeoti, J. E. Eweh, and M. Ugboja, “Approximate eigen solutions of DKP and Klein-Gordon equations with Hellmann potential,” Afr. Rev. Phys., 9 (006), 497-504, 2014
  • [16] A. N. Ikot, et al, “Analytical solutions of the DKP equation under Tietz-Hua potential in (1+ 3) dimensions,” Phys. Par. Nuc. Let., 12.2 (2015): 275-281, 2014.
  • [17] S. Zarrinkamar, H. Panahi, and M. Rezaei, “The generalized Coulomb interactions for relativistic scalar bosons,” Phys. Par. Nuc. Let., 13 (4), 436-441, 2016.
  • [18] O. J. Oluwadare and K. J. Oyewumi, “Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model,” EPJ A, 53 (2), 1-6, 2017.
  • [19] O. J. Oluwadare. and K. J. Oyewumi, “Approximate scattering state solutions of DKPE and SSE with Hellmann Potential,” Adv. H. E. Phys., 2018.
  • [20] H. Hassanabadi, B. Yazarloo, S. Zarrinkamar, and A. A. Rajabi, “Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction,” Phys. Rev. C, 84 (6), 064003, 2011.
  • [21] A. Taş and A. Havare, “Bound and Scattering States Solution of the Relativistic Spinless Particles in View of the Multiparameter Potential,” FBYS, 59 (4), 1-16, 2018.
  • [22] H. Yanar, A. Taş, M. Salti, and O. Aydogdu, “Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation,” EPJP, 135 (3), 1-14, 2020.
  • [23] N. Tazimi and A. Ghasempour, “Bound state solutions of three-dimensional Klein-Gordon equation for two model potentials by NU method,” Adv. H. E. Phys, 2020, Article ID 2541837, 2020.
  • [24] E. P. Inyang, E. P. Inyang, J. E. Ntibi, E. E. Ibekwe, and E. S. William, “Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method,” IJP, 1-7, 2020.
  • [25] I. L. Elviyanti, B. N. Pratiwi, A. Suparmi, and C. Cari, “The application of minimal length in Klein-Gordon equation with Hulthen potential using asymptotic iteration method,” AMP, 2018.
  • [26] A. N. Ikot, U. A. T. Okorie, C. A. Ngiangia, C. O. Onate, I. O. Edet, and P. O. Amadi, “Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method,” Ec. Q. J., 45 (1), 65-76, 2020.
  • [27] M. Eshghi, H. Mehraban, and M. Ghafoori, “Non‐relativistic Eigen spectra with q‐deformed physical potentials by using the SUSY approach,” Math. Met. App. Sci., 40 (4), 1003-1018, 2017.
  • [28] A. I. Ahmadov, S. M. Nagiyev, M. V. Qocayeva, K. Uzun, and V. A Tarverdiyeva, “Bound state solution of the Klein–Fock–Gordon equation with the Hulthén plus a ring-shaped-like potential within SUSY quantum mechanics,” IJMP A, 33 (33), 1850203, 2018.
  • [29] Z. Molaee, M. Ghominejad, H. Hassanabadi, and S. Zarrinkamar, “S-wave solutions of spin-one DKP equation for a deformed Hulthén potential in (1+ 3) dimensions,” EPJP, 127 (9), 1-8, 2012.
  • [30] M. K. Bahar and F. Yasuk, “Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky–Winternitz potential,” Ann. Phys., 344, 105-117, 2014.
  • [31] L. B. Castro, and A. S. De Castro, “Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations,” Phys. Rev. A., 90 (2), 022101, 2014.
  • [32] A. Tas, O. Aydogdu, and M. Salti, “Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism,” Ann. Phys., 379, 67-82, 2017.
  • [33] A. Tas, O. Aydogdu, and M. Salti, “Relativistic spinless particles with position dependent mass: Bound states and scattering phase shifts,” J. Kor. Phy. Soc., 70 (10), 896-904, 2018.
  • [34] S. Flugge, Practical Quantum Mechanics, 2nd ed., Springer-Verlag, Berlin, 189s., 1994.

Frost-Musulin Potansiyelinin Varlığında (1+3) Boyutta Duffin–Kemmer–Petiau Denkleminin l-Dalga Çözümleri

Year 2021, Volume: 16 Issue: 2, 444 - 457, 25.11.2021
https://doi.org/10.29233/sdufeffd.934867

Abstract

Bu çalışmada, spin-1 parçacıklar için Frost-Musulin potansiyelinin varlığında (1+3) boyutta Duffin-Kemmer-Petiau denkleminin analitik çözümleri elde edilmiştir. Bu çözümleri elde edebilmek için standart yöntem kullanılmış ve merkezcil terime bir yaklaşım uygulanmıştır. Elde edilen bağıntılar kullanılarak bağlı durum çözümleri Gauss hipergeometrik fonksiyonlar cinsinden ifade edilmiştir. Dalga fonksiyonların sınır koşulları kullanılarak herhangi bir l-durumu için bağlı durum enerji özdeğerlerini veren bağıntı türetilmiştir. Mathematica yazılım paketi kullanılarak herhangi bir l-durumu için bağlı durum enerji değerleri nümerik olarak belirlenmiştir. Ayrıca potansiyel parametrelerinin enerji özdeğerlerine olan etkileri grafiksel ve sayısal olarak incelenmiştir.

References

  • [1] N. Kemmer, “The particle aspect of meson theory,” Proc. of the Roy. Soc. of Lon., 173 (952), 91-116, 1939
  • [2] R. J. Duffin, “On the characteristic matrices of covariant systems,” Phys. Rev., 54 (12), 1114, 1938
  • [3] G. Petiau, “Contribution a la theorie des equations dondes corpusculaire,” Ph.D. Thesis, University of Paris, Published in Acad. Roy. de Belg., Classe Sci., Mem in 8, 16 (2), 1936.
  • [4] R. E. Kozack, B. C. Clark, S. Hama, V. K. Mishra, R. L. Mercer, and L. Ray, “Spin-one Kemmer-Duffin-Petiau equations and intermediate-energy deuteron-nucleus scattering,” Phys. Rev. C, 40 (5), 2181, 1989.
  • [5] V. Gribov, “QCD at large and short distances (annotated version),” EPJC, 10 (1), 71-90, 1999.
  • [6] Y. Nedjadi and R. C. Barrett, “On the properties of the Duffin-Kemmer-Petiau equation,” J. Phys. G, 19 (1), 87, 1993.
  • [7] Y. Nedjadi and R. C. Barrett, “The Duffin-Kemmer-Petiau oscillator,” J. Phys. A, 27 (12), 4301, 1994.
  • [8] Y. Nedjadi and R. C. Barrett, “Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson,” J. Math. Phys., 35 (9), 4517-4533, 1994.
  • [9] H. Hassanabadi, S. F. Forouhandeh, H. Rahimov, S. Zarrinkamar, and B. H. Yazarloo, “Duffin–Kemmer–Petiau equation under a scalar and vector Hulthen potential; an ansatz solution to the corresponding Heun equation,” Can. J. Phys., 90 (3), 299-304, 2012.
  • [10] M. Hamzavi and S. M. Ikhdair, “Approximate solution of the Duffin–Kemmer–Petiau equation for a vector Yukawa potential with arbitrary total angular momenta,” FBYS, 54 (11), 1753-1763, 2013.
  • [11] S. Zarrinkamar, A. A. Rajabi, B. H. Yazarloo, and H. Hassanabadi, “An approximate solution of the DKP equation under the Hulthén vector potential,” Chin. Phys. C, 37 (2), 023101, 2013.
  • [12] M. K. Bahar, “AIM solutions to the DKP equation for spin-1 particles in the presence of kratzer potential in (2+1) dimensions,” FBYS, 54 (11), 2133-2142, 2013.
  • [13] M. K. Bahar and F. Yasuk, “Relativistic spin-1 particles with position-dependent mass under the Coulomb interaction: Exact analytical solutions of the DKP equation,” Can. J. Phys., 91 (3), 191-197, 2013.
  • [14] M. K. Bahar and F. Yasuk, “Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential,” Can. J. Phys 92 (12), 1565-1569, 2014.
  • [15] C. A. Onate, J. O. Ojonubah, A. Adeoti, J. E. Eweh, and M. Ugboja, “Approximate eigen solutions of DKP and Klein-Gordon equations with Hellmann potential,” Afr. Rev. Phys., 9 (006), 497-504, 2014
  • [16] A. N. Ikot, et al, “Analytical solutions of the DKP equation under Tietz-Hua potential in (1+ 3) dimensions,” Phys. Par. Nuc. Let., 12.2 (2015): 275-281, 2014.
  • [17] S. Zarrinkamar, H. Panahi, and M. Rezaei, “The generalized Coulomb interactions for relativistic scalar bosons,” Phys. Par. Nuc. Let., 13 (4), 436-441, 2016.
  • [18] O. J. Oluwadare and K. J. Oyewumi, “Scattering state solutions of the Duffin-Kemmer-Petiau equation with the Varshni potential model,” EPJ A, 53 (2), 1-6, 2017.
  • [19] O. J. Oluwadare. and K. J. Oyewumi, “Approximate scattering state solutions of DKPE and SSE with Hellmann Potential,” Adv. H. E. Phys., 2018.
  • [20] H. Hassanabadi, B. Yazarloo, S. Zarrinkamar, and A. A. Rajabi, “Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction,” Phys. Rev. C, 84 (6), 064003, 2011.
  • [21] A. Taş and A. Havare, “Bound and Scattering States Solution of the Relativistic Spinless Particles in View of the Multiparameter Potential,” FBYS, 59 (4), 1-16, 2018.
  • [22] H. Yanar, A. Taş, M. Salti, and O. Aydogdu, “Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation,” EPJP, 135 (3), 1-14, 2020.
  • [23] N. Tazimi and A. Ghasempour, “Bound state solutions of three-dimensional Klein-Gordon equation for two model potentials by NU method,” Adv. H. E. Phys, 2020, Article ID 2541837, 2020.
  • [24] E. P. Inyang, E. P. Inyang, J. E. Ntibi, E. E. Ibekwe, and E. S. William, “Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method,” IJP, 1-7, 2020.
  • [25] I. L. Elviyanti, B. N. Pratiwi, A. Suparmi, and C. Cari, “The application of minimal length in Klein-Gordon equation with Hulthen potential using asymptotic iteration method,” AMP, 2018.
  • [26] A. N. Ikot, U. A. T. Okorie, C. A. Ngiangia, C. O. Onate, I. O. Edet, and P. O. Amadi, “Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method,” Ec. Q. J., 45 (1), 65-76, 2020.
  • [27] M. Eshghi, H. Mehraban, and M. Ghafoori, “Non‐relativistic Eigen spectra with q‐deformed physical potentials by using the SUSY approach,” Math. Met. App. Sci., 40 (4), 1003-1018, 2017.
  • [28] A. I. Ahmadov, S. M. Nagiyev, M. V. Qocayeva, K. Uzun, and V. A Tarverdiyeva, “Bound state solution of the Klein–Fock–Gordon equation with the Hulthén plus a ring-shaped-like potential within SUSY quantum mechanics,” IJMP A, 33 (33), 1850203, 2018.
  • [29] Z. Molaee, M. Ghominejad, H. Hassanabadi, and S. Zarrinkamar, “S-wave solutions of spin-one DKP equation for a deformed Hulthén potential in (1+ 3) dimensions,” EPJP, 127 (9), 1-8, 2012.
  • [30] M. K. Bahar and F. Yasuk, “Relativistic solutions for the spin-1 particles in the two-dimensional Smorodinsky–Winternitz potential,” Ann. Phys., 344, 105-117, 2014.
  • [31] L. B. Castro, and A. S. De Castro, “Corroborating the equivalence between the Duffin-Kemmer-Petiau and the Klein-Gordon and Proca equations,” Phys. Rev. A., 90 (2), 022101, 2014.
  • [32] A. Tas, O. Aydogdu, and M. Salti, “Dirac particles interacting with the improved Frost–Musulin potential within the effective mass formalism,” Ann. Phys., 379, 67-82, 2017.
  • [33] A. Tas, O. Aydogdu, and M. Salti, “Relativistic spinless particles with position dependent mass: Bound states and scattering phase shifts,” J. Kor. Phy. Soc., 70 (10), 896-904, 2018.
  • [34] S. Flugge, Practical Quantum Mechanics, 2nd ed., Springer-Verlag, Berlin, 189s., 1994.
There are 34 citations in total.

Details

Primary Language Turkish
Subjects Metrology, Applied and Industrial Physics
Journal Section Makaleler
Authors

Ahmet Tas 0000-0002-1226-5634

Publication Date November 25, 2021
Published in Issue Year 2021 Volume: 16 Issue: 2

Cite

IEEE A. Tas, “Frost-Musulin Potansiyelinin Varlığında (1+3) Boyutta Duffin–Kemmer–Petiau Denkleminin l-Dalga Çözümleri”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 16, no. 2, pp. 444–457, 2021, doi: 10.29233/sdufeffd.934867.