Various Parity-State Solutions of Spin-One DKP Equation with Cornell and Exponential Interaction; The Laplace Transform Approach

Document Type : Original Article


1 Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

2 Department of Physics, University of Guilan, Rasht, Iran


We consider the spin-one DKP equation in the presence of vector Cornell and exponential interactions which are among successful interactions of particle physics. We obtain the exact analytical solutions of the former and the approximate solutions the latter via the Laplace integral transform method in terms of Hypergeometric functions for arbitrary quantum number in three spatial dimensions.


Main Subjects

[1] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Publications) 1972.
[2] A. Arda, R. Sever, Exact solutions of the Schrödinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials, Journal of Mathematical Chemistry, 50 2012, 971-980.
[3] C. Berkdemir, Pseudospin symmetry in the relativistic Morse potential including the spin–orbit coupling term, Nuclear Physics A, 770(1-2) 2006, 32-39.
[4] R.C. Barret, Y. Nedjadi, Meson-nuclear interactions in the Duffin-Kemmer-Petiau formalism, Nuclear Physics A, 585(1) 1995, 311-312.
[5] T.R. Cardoso, L.B. Castro, A.S. de Castro, On the nonminimal vector coupling in the Duffin–Kemmer–Petiau theory and the confinement of massive bosons by a linear potential, Journal of Physics A: Mathematical and Theoretical, 43(5) 2010, 055306.
[6] L.B. Castro, Quantum dynamics of scalar bosons in a cosmic string background, The European Physical Journal C, 75(6) 2015, 287.
[7] Y. Chargui, A. Dhahbi, An extended version of the spin-one Duffin–Kemmer–Petiau oscillator, Physica Scripta 96(7) 2021, 075003.
[8] L.B. Castro, Luiz P. de Oliveira, Remarks on the Spin-One Duffin-Kemmer-Petiau Equation in the Presence of Nonminimal Vector Interactions in Dimensions, Advances in High Energy Physics 2014
[9] R.J. Duffin, On the characteristic matrices of covariant systems, Physical Review, 54(12) 1938, 1114.
[10] B. Hamil, B.C. Lütfüo─člu, H. Aounallah, The spin-one DKP equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum, Modern Physics Letters A, 36(4) 2021, 2150021.
[11] N. Kemmer, Quantum theory of Einstein-Bose particles and nuclear interaction, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 166(924) 1938, 127-153.
[12] M. de Montigny, E.S. Santos, On the Galilean Duffin-Kemmer-Petiau equation in arbitrary dimensions, International Journal of Modern Physics A, 35(18) 2020, 2050086.
][13] H.F. Nogueira, A.S. de Castro, D.R.M. Pimentel, A large class of bound-state solutions of the Schrödinger equation via Laplace transform of the confluent hypergeometric equation, Journal of Mathematical Chemistry, 54 2016, 1287-1295.
[14] Y. Nedjadi, R.C. Barret, Solution of the central field problem for a Duffin–Kemmer–Petiau vector boson, Journal of Mathematical Physics, 35(9) 1994, 4517-4533
[15] S. Ortakaya, Pseudospin symmetry in position-dependent mass dirac-coulomb problem by using laplace transform and convolution integral, Few-Body Systems, 54(11) 2013, 2073-2080.
[16] G. Petiau, University of Paris thesis, published in Academie Royale de Medecine de Belgique, Classe des Sciences, Memoires in 80 (16) 1936.
[17] K. Sogut et al Creation of vector bosons by an electric field in curved spacetime, Annals of Physics, 343, 2014, 40-48.
[18] H. Sobhani, H. Hassanabadi, W.S. Chung, Study of Spin-1 Particles Scattering and Bound States in the q-Deformed Quantum Mechanics, Few-Body Systems, 61 2020, 1-12.
[19] C.D. White, The Cornell potential from general geometries in AdS/QCD, Physics Letters B, 652(2-3) 2007, 79-85.
[20] Ch. Y. Wong, Molecular states of heavy quark mesons, Physical Review C, 69(5) 2004, 055202.