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

Yıl 2016, Cilt: 29 Sayı: 4, 937 - 946, 19.12.2016

Akpan Ndem Ikot Eser Olgar H. Hassanabadi

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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)