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THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL

Year 2016, Volume: 29 Issue: 4, 937 - 946, 19.12.2016

Abstract

In this paper, we study the Schrödinger equation with the generalized Hulthen potential plus a new ring shaped potential. We obtained approximately the bound state energy spectra and the corresponding wave function using the functional analysis method. We use the well-known Hellmann-Feynmann theorem to calculate the expectation values for  ,,  and .We also discussed the special case of the potential which is consistent with the results found in the literature.

References

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  • L.D.Landau and E.M.Lifshitz, Quantum Mechnaics,Non-RelativisticTheory
  • (Pergamon,New York, 1977)
  • S.H.Dong, Wave Equations in Higher Dimensions(Springer,Dordrecht,2011)
  • C Berkdemir and R Sever,J.Math.Chem.46 1122 (2009)
  • H Hartmann and D Schuch,Int.J.Quant.Chem.18 125 (1980)
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  • Gh.E.Draganascu, C.Campigotto and K.Kibler,Phys.Lett.A 170 339(1992)
  • H Hassanabadi,A N Ikot and S Zarrinkamar, Acta Phys.Polo.A 126(2014)647
  • M.C.Zhang,B.An and H.F.Guo-Qing,J.Math.Chem.48 876 (2010)
  • M.V.Carpio-Bernido and C.C.Bernido,Phys.Lett.A 134,395(1989)
  • H.Hartman,Theor.Chim.Acta 24,201(1972)
  • S.H.Dong,G.H.Sun and M.Lozada-Cassou,Phys.Lett.A 328,299(2004)
  • G.Q.Huang-Fu and M.C.Zhang,J.Math.Phys.52,042108(2011)
  • F.L.Lu and C.Y.Chen,Chin.Phys.B 19,100309(2010)
  • C.Y.Chen,C.L.Liu and F.L.Lu, Phys.Lett.A 374,1346(2010)
  • C.Y.Chen,Y.You,X.H.Wang and S.H.Dong,Phys.lett.A 377,1521(2013)
  • M.C.Zhang and Z.C.Liu,J.Math.Phys. 53,082104 (2012)
  • A.N.Ikot,H.Hassanabadi,H.P.Obong and Y.C.Umoren, Z.Naturforsch,69a,659(2014)
  • M.Eshghi,Chin.Phys.Lett.29,110304(2012)
  • W.C.Qiang,Chin.Phys.12 136(2003)
  • C.Y.Chen,F.L.Lu and D.S.Sun,Commun.Theor.Phys.45,889(2006)
  • M.C.Zhang,J.Math.Chem,Doi:10.1007/s10910-012-055-1
  • C.Berkdemir,J.Math.Chem.46,139(2009)
  • C.Y.Chen,F.L.Lu,D.S.Sun,Y.You and S.H.Dong,App.Math.Lett.40,90(2015)
  • D.S.Sun,Y.You,F.L.Lu,C.Y.Chen and S.H.Dong,Phys.Scr.89,045002(2014)
  • C.Y.Chen,F.L.Lu,D.S.Sun and S.H.Dong,Chin.Phys.B 22,100302(2013)
  • M Abramowitz and I AStegunHand book of Mathematical Functions
  • (New York Dover) (1970)
  • C.S.Jia,Y.Li,Y.Sun,J.Y.Liu and L.T.Sun,Phys.Lett.A 311,115(2003)
  • I.S.Gradsteyn and I.M.Ryzhik,Tables of Integrals,Series, and Product,Academic Press,
  • New York(2000)
  • C.S.Jia,J.Y.Liu and P.Q.Wang,Phys.Lett.A 372,4779(2008)
  • A.N.Ikot,T.M.Abbey,E.O.Chukwuocha and M.C.Onyeaju, Can.J.Phys.Doi:1139/cjp-
  • -0066
  • L.I Schiff,Quantum Mechanics,McGraw-Hill,New York New (1955)
  • R.Rahimov,H.Nikoofard,S.Zarrinkamar and H.Hassanabadi, App.Math.Comp.
  • , 4710(2013)
  • D.Agboola,Acta Phys.Polo.A 120 ,371(2011)
  • S.M.Ikhdair and R.Sever,arxiv:0704.0489v1[quant-ph]2007
  • F.L.Lu,C.Y.Chen and Y.You,Acta Phys.Sin.62,200301(2013)
Year 2016, Volume: 29 Issue: 4, 937 - 946, 19.12.2016

Abstract

References

  • S.H.Dong, Factorization Method in Quantum Mechanics(Springer,Netheland,2007)
  • L.D.Landau and E.M.Lifshitz, Quantum Mechnaics,Non-RelativisticTheory
  • (Pergamon,New York, 1977)
  • S.H.Dong, Wave Equations in Higher Dimensions(Springer,Dordrecht,2011)
  • C Berkdemir and R Sever,J.Math.Chem.46 1122 (2009)
  • H Hartmann and D Schuch,Int.J.Quant.Chem.18 125 (1980)
  • M Aktas, J.Math.Chem.49(2011)1831
  • M Kibler and P Winternitz,J .Phys.A:Math.Gen.20 4097 (1987)
  • Gh.E.Draganascu, C.Campigotto and K.Kibler,Phys.Lett.A 170 339(1992)
  • H Hassanabadi,A N Ikot and S Zarrinkamar, Acta Phys.Polo.A 126(2014)647
  • M.C.Zhang,B.An and H.F.Guo-Qing,J.Math.Chem.48 876 (2010)
  • M.V.Carpio-Bernido and C.C.Bernido,Phys.Lett.A 134,395(1989)
  • H.Hartman,Theor.Chim.Acta 24,201(1972)
  • S.H.Dong,G.H.Sun and M.Lozada-Cassou,Phys.Lett.A 328,299(2004)
  • G.Q.Huang-Fu and M.C.Zhang,J.Math.Phys.52,042108(2011)
  • F.L.Lu and C.Y.Chen,Chin.Phys.B 19,100309(2010)
  • C.Y.Chen,C.L.Liu and F.L.Lu, Phys.Lett.A 374,1346(2010)
  • C.Y.Chen,Y.You,X.H.Wang and S.H.Dong,Phys.lett.A 377,1521(2013)
  • M.C.Zhang and Z.C.Liu,J.Math.Phys. 53,082104 (2012)
  • A.N.Ikot,H.Hassanabadi,H.P.Obong and Y.C.Umoren, Z.Naturforsch,69a,659(2014)
  • M.Eshghi,Chin.Phys.Lett.29,110304(2012)
  • W.C.Qiang,Chin.Phys.12 136(2003)
  • C.Y.Chen,F.L.Lu and D.S.Sun,Commun.Theor.Phys.45,889(2006)
  • M.C.Zhang,J.Math.Chem,Doi:10.1007/s10910-012-055-1
  • C.Berkdemir,J.Math.Chem.46,139(2009)
  • C.Y.Chen,F.L.Lu,D.S.Sun,Y.You and S.H.Dong,App.Math.Lett.40,90(2015)
  • D.S.Sun,Y.You,F.L.Lu,C.Y.Chen and S.H.Dong,Phys.Scr.89,045002(2014)
  • C.Y.Chen,F.L.Lu,D.S.Sun and S.H.Dong,Chin.Phys.B 22,100302(2013)
  • M Abramowitz and I AStegunHand book of Mathematical Functions
  • (New York Dover) (1970)
  • C.S.Jia,Y.Li,Y.Sun,J.Y.Liu and L.T.Sun,Phys.Lett.A 311,115(2003)
  • I.S.Gradsteyn and I.M.Ryzhik,Tables of Integrals,Series, and Product,Academic Press,
  • New York(2000)
  • C.S.Jia,J.Y.Liu and P.Q.Wang,Phys.Lett.A 372,4779(2008)
  • A.N.Ikot,T.M.Abbey,E.O.Chukwuocha and M.C.Onyeaju, Can.J.Phys.Doi:1139/cjp-
  • -0066
  • L.I Schiff,Quantum Mechanics,McGraw-Hill,New York New (1955)
  • R.Rahimov,H.Nikoofard,S.Zarrinkamar and H.Hassanabadi, App.Math.Comp.
  • , 4710(2013)
  • D.Agboola,Acta Phys.Polo.A 120 ,371(2011)
  • S.M.Ikhdair and R.Sever,arxiv:0704.0489v1[quant-ph]2007
  • F.L.Lu,C.Y.Chen and Y.You,Acta Phys.Sin.62,200301(2013)
There are 42 citations in total.

Details

Journal Section Physics
Authors

Akpan Ndem Ikot

Eser Olgar This is me

H. Hassanabadi This is me

Publication Date December 19, 2016
Published in Issue Year 2016 Volume: 29 Issue: 4

Cite

APA Ikot, A. N., Olgar, E., & Hassanabadi, H. (2016). THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL. Gazi University Journal of Science, 29(4), 937-946.
AMA Ikot AN, Olgar E, Hassanabadi H. THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL. Gazi University Journal of Science. December 2016;29(4):937-946.
Chicago Ikot, Akpan Ndem, Eser Olgar, and H. Hassanabadi. “THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL”. Gazi University Journal of Science 29, no. 4 (December 2016): 937-46.
EndNote Ikot AN, Olgar E, Hassanabadi H (December 1, 2016) THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL. Gazi University Journal of Science 29 4 937–946.
IEEE A. N. Ikot, E. Olgar, and H. Hassanabadi, “THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL”, Gazi University Journal of Science, vol. 29, no. 4, pp. 937–946, 2016.
ISNAD Ikot, Akpan Ndem et al. “THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL”. Gazi University Journal of Science 29/4 (December 2016), 937-946.
JAMA Ikot AN, Olgar E, Hassanabadi H. THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL. Gazi University Journal of Science. 2016;29:937–946.
MLA Ikot, Akpan Ndem et al. “THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL”. Gazi University Journal of Science, vol. 29, no. 4, 2016, pp. 937-46.
Vancouver Ikot AN, Olgar E, Hassanabadi H. THE ANALYTICAL SOLUTIONS OF THE SCHRODINGER EQUATION WITH GENERALIZED HULTHEN PLUS A NEW RING SHAPED LIKE POTENTIAL. Gazi University Journal of Science. 2016;29(4):937-46.