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

Akpan Ndem Ikot , Eser Olgar H. Hassanabadi

https://izlik.org/JA83EW87KW

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.

Keywords

: Schrödinger equation , generalized Hulthen potential , new ring shaped potential , Hellmann-Feynmann Theorem ,

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)