Abstract
We study the D-dimensional Klein-Gordon equation for the modified Hylleraas potential with position dependent mass. We obtain the energy eigenvalues and the corresponding eigenfunctions for any arbitrary l-state using the parametric Nikiforov-Uvarov method. New elegant approximation method is used to deal with the centrifugal term. We also discuss the two limiting cases of this potential, i.e. the Woods-Saxon and Rosen-Morse potentials.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Xiang J.G.: Non-hypergeometric-type of polynomials and solutions of Schrodinger equation with position-dependent mass. Commun.Theor.Phys. 56, 235 (2011)
Gonul B., Gonul B., Tuteu D., Ozer O.: Supersymmetric approach to exactly solvable systems with position-dependent masses. Mod.Phys.Lett.A 17, 2057 (2002)
de Souza Dutra A., Almeida C.A.S.: Exact solvability of potentials with spatially dependent efffective masses. Phys. Lett. A 275, 25 (2000)
Gonul B., Ozer O., Gonul B., Uzgun F.: Exact solutions of effective mass Schrodinger equations. Mod. Phys. Lett. A 17, 2453 (2002)
Alhaidari A.D.: Solutions of the non-relativistic wave equations with position-dependent effective mass. Phys. Rev. A 66, 042116 (2002)
Jiang Y., Dong S.H., Sun G.H.: Series solutions of schrodinger equation with position-dependent mass for the morse potential. Phys. Lett. A 322, 290 (2004)
Koc R., Koca M.: A systematic study on the exact solution of the position dependent mass Schrodinger equation. J. Phys. Math. Gen. 36, 8105 (2003)
Bagchi B., Banerjee A., Quesne C., Thachuk V.M.: Deformed shape invariance and exactly solvable hamiltonians with position-dependent effective mass. J. Phys. A Math. Gen. 38, 2929 (2005)
Ju G.X., Xiang Y., Ren Z.Z.: Localization of s-wave and quantum effective potential of a quasi-free particle with position-dependent mass. Commun. Theor. Phys. 46, 819 (2006)
Bagchi B., Gorain P., Quesne C.: Morse potential and its relationship with the coulomb in a position-dependent mass. Mod. Phys. Lett. A 21, 2703 (2006)
Nikiforov A.F., Uvarov V.B.: Special functions of mathematical physics. Birkhause, Basel (1988)
Dong S.H.: Factorization method in quantum mechanics. Springer, Dordrecht (2007)
Alhassid Y., Wu J.: An algebraic approach to morse potential scattering. Chem. Phys. Lett 56, 81 (1984)
Cooper F., Freeman B.: Aspect of supersymmetric quantum mechanics. Ann. Phys. 146, 262 (1983)
Fakhri H.: Shape invariance symmetries for quantum states of the superpotentials A tanh \({\left({\omega}y\right) + \frac{B}{A} \, {\rm and} \, -A \, {\rm cot} \, \omega{\theta} + B \, {\rm csc} \, \omega{\theta}}\) . Phys. Lett. A 324, 366 (2004)
De R., Butt R., Sukhatme U.: Mapping of shape invariant potential under point canonical transformation. J. Phys. A Math. Gen. 25, L843 (1992)
Cooper F., Khare A., Sukhatme U.: Supersymmetry and quantum mechanics. Phys. Rep. 251, 267 (1995)
Dong S.H., Sun G.H.: The series solutions of the non-relativistic equation with the morse potential. Phys. Lett. A 314, 261 (2003)
Oyewumi K.J., Akinpelu F.O., Agboola A.D.: Exactly complete solution of the pseudoharmonic potential in n-dimension. Int. J. Theor. Phys. 47, 1039 (2008)
Hassanabadi H., Zarinkamar S., Rajabi A.A.: Exact solutions of D-dimensional Schrodinger equation for an energy-dependent potential By NU method. Commun. Theor. Phys. 55, 541 (2011)
Hylleraas E.A.: Energy Formula and Potential Distribution of Diatomic Molecules. J.Chem.Phys. 3, 595 (1938)
Varshni Y.: Comparative study of potential of potential energy functions for diatomic molecules. Rev. Mod. Phys. 29(4), 664 (1957)
Hassanabadi H., Zarinkamar S., Rahimov H.: Approximate solution of D-dimensional Klein-Gordon equation with hulthen-type potential via SUSYQM. Commun. Theor. Phys. 56, 423 (2011)
Tezcan C., Sever R.: A general approach for the exact solution of the Schrodinger Equation. Int. J. Theor. Phys. 48, 337 (2009)
Hill E.L.: The theory of vector spherical harmonics. Am. J. Phys. 22, 211 (1954)
Ikot A.N., Akpabio L.E., Obu J.A.: Exact solution of Schrodinger equation with five-parameter exponential-type potential. J. Vect. Relat. 6(1), 1 (2011)
Ikot A.N., Akpabio L.E., Uwah E.J.: Bound state solutions of the Klein-Gordon Equation with hulthen potential. EJTP 8(25), 225 (2011)
Oyewumi, K.J., Akoshile, C.O.: Bound State Soultions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry. Euro. Phys. J. A 45 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ikot, A.N., Awoga, O.A., Antia, A.D. et al. Approximate Solutions of D-Dimensional Klein-Gordon Equation with modified Hylleraas Potential. Few-Body Syst 54, 2041–2051 (2013). https://doi.org/10.1007/s00601-013-0706-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-013-0706-1