Analytical solutions of Schrödinger equation with new solvable potential family V(r)=A/r^2-B/r+Cr^(δ+1) via Nikiforov-Uvarov (NU) method

Akaninyene Daniel Antia, Ita Okon Akpan, Akpan Ndem Ikot, Elham Maghsoodi, Saber Zarrinkamar, Hassan Hassanabadi

Abstract


In this paper, we have presented the exact solutions of the Schrödinger equation with the family of potentials V(r)=A/r^2-B/r+Cr^(δ+1). We have obtained the energy eigenvalues and the corresponding wave functions expressed in terms of the associated Laguerre polynomials for  using the Nikiforov-Uvarov (NU) method. The energy levels for each case is computed for diatomic molecules H2, CO, NO and N2  for various values of and . We have also computed the expectation values of, and the Virial theorem using the Hellmann-Feynmann theorem (HFT).

Keywords


Schrödinger equation; Energy eigenvalue; Eigenfunction; Diatomic molecules; Hellmann-Feynmann theorem

Full Text:

PDF

References


S. Meyur, S. Debnath, Bulg. J. Phys. 2008,35 , 290

A. D.Antia,A. N. Ikot and L.E.Akpabio,Euro.J.Sci.Res.2010 ,46 ,107

A. N.Ikot and L. E.Akpabio,Appl.Phys.Res.2010, 2 ,202.

A. N.Ikot,A.D.Antia,L.E.Akpabio and J.A.Obu,J.Vect.Relat. 2011 6 65.

A. N. Ikot ,L. E.Akpabio and J.A.Obu,J.Vect.Relat.2011 6 1

A. N. Ikot and L. E.Akpabio,Int.Rev.Phys.2010 4 224

S. M. Ikhdair and R. Sever, J. Mol. Struct. – Theochem 2008 855 13

S. H. Dong, Appl. Math. Lett.. 2003 16 199.

M. L. Sage, Chem. Phys. 1984 87 431

M. M. Neito, Am. J. Phys.1979 47 1067.

S. M. Ikhdair and R. Sever, J. Math. Chem.2009 45 1137

S. Ikhdair and R. Sever, J. Mol. Struct.-Theochem 2007 806 155.

C. L. Pekeris, Phys. Rev. 1934 45 98.

C. Berkdemir, Nucl. Phys A 2006 770 32.

W. C. Qiang and S. H. Dong, Phys. Lett. A2007 363 169.

C. Berkdemir and J. Han, Chem. Phys. Lett.2005 409 203

C. Berkdemir and A. Berkdemir and J. Han, Chem. Phys. Lett. 2006 417 326.

P. M. Morse, Phys. Rev. 1929 34 57

M. Simsek and H. Egrifes, J. Phys. A: Math Gen. 2004 37 4379

B. Goniil and I. Zorba, Phys. Lett. A 2000 269 83

L. Hulthen, Ark. Mat. Astron Fys. A 1942 28 5.

O. Yesitas, Phys. Scr.2007 75 41.

G. Poschl and E. Teller , Z. Phys.1933 83 143

S. M. Ikhdair and R. Sever, Int. J. Mod. Phys. E 2008 17 1107

Y. F. Cheng and T. Q. Dai, Phys. Scr.2007 75 274

W. C. Qiang, Chin. Phys.2004 13 575

L. Z. Yi, Y. F. Diao, J. Y. Liu and C. S. Jia, Phys. Lett. A 2004 333 212

N. Rosen and P. M. Morse, Phys. Rev.1932 42 210

A. Khare, U. Sukhatme ,J. Phys. A: Math. Gen.1998 21 L501

S. Flugge ,Practical Quantum Mechanics(Springer,Berlin,1974)

J. Sadeghi and B. Pourhassan, EJTP 2008 5 193

D. A. Morales, Chem. Phys. Lett. 2004 394 68.

E. D. Filho and R. M. Ricotta, Phys. Lett. A 2000 269 269

A. Diaf, A. Chouchaoui and R. L. Lombard, Ann. Phys.2005 317 354.

O. Bayrak, I. Boztosun and H. Ciftci , Int. J. Quant. Chem.2007 107 540

J. P. Kilingbeck, A. Grosjean and G.Jolicard, J. Chem. Phys.2002 116 447.

D. A. Morales,Chem. Phys. Lett.1989 161, 253.

K. J. Oyewumi, Int. J. Theor. Phys.2010 49 1302

M. Badawi, N. Bessis and G. Bessis , J. Phys. B. Atom. Molec. Phys.1972 5 L157.

A. F. Nikiforov and V. B. Uvarov (Special Fucntions of Mathematical Physics, Basel, Birkhauser, 1988)

C. Berkdemir (Theoretical Concepts of Quantum Mechanics. ISBN 978-953-51-0088-1. Chapter 11, Application of the Nikiforov-Uvarov Method in Quantum Mechanics, Edited by: Mohammad Reza Pahlavani. Publisher: InTech, February 2012. 22.)

M. Aygun, O. Bayrak and I. Boztosun, solution of the radial Schrödinger Equation for the potential family using the asymptotic iteration method, arxiv: math – ph/0703040v 13 March 2007.

J. E. Avron, Ann. Phys.1991 131 73.

M. Taut, J. Phys. A: Math. Gen.1995 28 2081

H. Ciftci, R. L. Hall and Q. D. Katatbeh, J. Phys. A: Math. Gen.2003 36 7001.

E. Castro and P. Martin, J. Phys. A: Math. Gen.2000 33 5321.

C. Berkdemir and R. Sever,J.Maths.Chem.2009 46 1122.

G. Marc and W. G.Mcmillam, Adv.Chem.Phys.1985 58 205.

K. J. Oyewumi, Found.Phys.Lett.2005 18 1

D. Agboola, Acta Physica Polonica A 2011 120 371.

E. Castro, J. L. Paz and P. Martin, J. Mol. Struc: Theochem.2006 15 769.

S. Y. P. Varshni, Chem.Phys.2008 32 353.




DOI: http://dx.doi.org/10.17951/aaa.2015.70.167
Data publikacji: 2016-04-29 12:28:33
Data złożenia artykułu: 2016-01-08 16:06:21

Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Akaninyene Daniel Antia, Ita Okon Akpan, Akpan Ndem Ikot, Elham Maghsoodi, Saber Zarrinkamar, Hassan Hassanabadi

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.