Abstract
We present the approximate analytical solutions of Duffin–Kemmer–Petiau equation with a vector Hellmann potential for spin-zero particles. The energy eigenvalues and the corresponding eigenfunctions are obtained in closed form and some numerical results are included.
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Petiau, G.: Phd Thesis, University of Paris, 1936; Acad. R. Belg. Cl. Sci. Mem. Collect. 8, 16 (1936)
Kemmer N.: Quantum theory of Einstein-Bose particles and nuclear interaction. Proc. R. Soc. A 166, 127–153 (1938)
Duffin R.J.: On the characteristic matrices of covariant systems. Phys. Rev. 54, 1114 (1938)
Boumali A.: On the eigensolutions of the one-dimensional Duffin-Kemmer-Petiau oscillator. J. Math. Phys. 49, 022302 (2008)
Kanatchikov I.V.: On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory. Rep. Meth. Phys. 46, 107–112 (2000)
Boumali A.: Particule de spin 0 dans un potential d’Aharonov-Bohm. Can. J. Phys. 82, 67–74 (2004)
Boumali A.: Particule de spin-1 dans un potential d’Aharonov-Bohm. Can. J. Phys. 85, 1417–1429 (2007)
de Montigny M. et al.: Galilean covariance and the Duffin-Kemmer-Petiau equation. J. Phys. A 33, L273–L278 (2000)
Lunardi J.T. et al.: Remarks on Duffin-Kemmer-Petiau theory and gauge invariance. Phys. Lett. A 268, 165–173 (2000)
Lunardi J.T. et al.: Duffin-Kemmer-Petiau theory in the causal approach. Int. J. Mod. Phys. A 17, 205–227 (2000)
Kerr L.K. et al.: Theoretical and experimental K+ + nucleus total and reaction cross sections from the KDP-RIA model. Prog. Theor. Phys. 103, 321–335 (2000)
Boumali A., Chetouani L.: Exact solutions of the Kemmer equation for a Dirac oscillator. Phys. Lett. A 346, 261–268 (2005)
Boumali A.: One-dimensional thermal properties of the Kemmer oscillator. Phys. Scr. 76, 669 (2007)
Nedjadi Y., Barrett R.C.: The Duffin-Kemmer-Petiau oscillator. J. Phys. A Math. Gen. 27, 4301 (1994)
Boutabia-Cheraitia B., Boudjedaa T.: Solution of DKP equation in Woods-Saxon potential. Phys. Lett. A 338, 97–107 (2005)
Hassanabadi, S., Rajabi, A.A., Yazarloo, B.H., Zarrinkamar, S., Hassanabadi, H.: Adv. Quasi-analytical solutions of DKP equation under the Deng-Fan interaction. High Energy Phys. 2012, Article ID 804652. doi:10.1155/2012/804652
Oudi R., Hassanabadi S., Rajabi A.A., Hassanabadi H.: Approximate bound state solutions of DKP equation for any J state in the presence of Woods-Saxon potential. Commun. Theor. Phys. 57, 15–18 (2012)
Yasuk F., Berkdemir C., Berkdemir A., Onem C.: Exact solutions of the Duffin-Kemmer-Petiau equation for the deformed Hulthen potential. Phys. Scr. 71, 340 (2005)
Boztosun I., Karakoc M., Yasuk F., Durmus A.: Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation. J. Math. Phys. 47, 062301 (2006)
Hassanabadi H., Molace Z., Boumali A.: Exact solutions of the Duffin-Kemmer-Petiau equation with a hyperbolical potential in (1+3) Dimensions. Chin. Phys. C 37, 073104 (2013)
Hellmann H.: Acta Physicochim. URS 1, 193 (1935)
Dutt R., Mukherji U., Varshni Y.P.: Shifted large-N expansion for the bound states of the Hellmann potential. Phys. Rev. A 34, 777–784 (1986)
de Castro A.S.: Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential. J. Phys. A Math. Theor. 44, 035201 (2011)
Molaee Z., Bahar M.K., Yasuk F., Hassanabadi H.: Solutions of the Duffin Kemmer Petiau equation in the presence of Hulthén potential in (1+2) dimensions for unity spin particles using the asymptotic iteration method. Chin. Phys. B 22, 060306 (2013)
Nikiforov A.F., Uvarov V.B.: Special functions of Mathematical Physics. Birkhauser, Basel (1988)
Zarrinkamar S., Rajabi A.A., Yazarloo B.H., Hassanabadi H.: An approximate solution of the DKP equation under the Hulthén vector potential. Chin. Phys. C 37, 023101 (2013)
Greene R.L., Aldrich C.: Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14, 2363–2366 (1976)
Abramowitz M., Stegun I.A.: Handbook of Mathematical Function with Formulaes, Graphs and Mathematical tables. Dover, New York (1972)
Grabdshteyn I.S., Ryzhik I.M.: Tables of Integrals, Series and Products. AP, New York (1980)
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Ikot, A.N., Hassanabadi, H., Zarrinkamar, S. et al. Solutions of the Duffin–Kemmer–Petiau Equation Under a Vector Hellman Potential. Few-Body Syst 55, 211–218 (2014). https://doi.org/10.1007/s00601-014-0837-z
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DOI: https://doi.org/10.1007/s00601-014-0837-z