On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

• Authors: Sameer Ikhdair , Ramazan Sever
• Languages of publication: EN

Abstracts

EN

Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

Keywords

EN

bound states; pseudoharmonic potential; Kratzer’s potential; Mie-type potential; anharmonic oscillator potential; Schrödinger equation; diatomic molecules

Discipline

• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 03.65.Ge: Solutions of wave equations: bound states

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 697-703

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Sameer Ikhdair

• Department of Physics, Near East University, Nicosia, North Cyprus, Mersin-10, Turkey

author

Ramazan Sever

• Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

References

• [1] S. Özçelik, M. Şimşek, Phys. Lett. A 152, 145 (1991) http://dx.doi.org/10.1016/0375-9601(91)91081-N[Crossref]
• [2] S.-H. Dong, Physica Scripta 64, 273 (2001) http://dx.doi.org/10.1238/Physica.Regular.064a00273[Crossref]
• [3] S.-H. Dong, Z.-Q. Ma, J. Phys. A 31, 9855 (1998) http://dx.doi.org/10.1088/0305-4470/31/49/009[Crossref]
• [4] M.S. Child, S.-H. Dong, X.-G. Wang, J. Phys. A 33, 5653 (2000) http://dx.doi.org/10.1088/0305-4470/33/32/303[Crossref]
• [5] S.-H. Dong, Int. J. Theor. Phys. 39, 1119 (2000) http://dx.doi.org/10.1023/A:1003614810934[Crossref]
• [6] S.-H. Dong, Int. J. Theor. Phys. 40, 569 (2001) http://dx.doi.org/10.1023/A:1004171912938[Crossref]
• [7] S. Flügge, Practical Quantum Mechanics 1 (Springer, Berlin, 1994)
• [8] S.-H. Dong, Physica Scripta 65 (2002) 289. http://dx.doi.org/10.1238/Physica.Regular.065a00289[Crossref]
• [9] S. Ikhdair, R. Sever, J. Mol. Struct. (Theochem) 806, 155 (2007) http://dx.doi.org/10.1016/j.theochem.2006.11.019[Crossref]
• [10] K.J. Oyewumi, E.A. Bangudu, Arabian J. Sci. Eng. 28 (2A), 173 (2003)
• [11] P.M. Morse, Phys. Rev. 34, 57 (1929) http://dx.doi.org/10.1103/PhysRev.34.57[Crossref]
• [12] A. Kratzer, Z. Phys. 3, 289 (1920) http://dx.doi.org/10.1007/BF01327754[Crossref]
• [13] E. Fues, Ann. Physik 80, 367 (1926) http://dx.doi.org/10.1002/andp.19263851204[Crossref]
• [14] K.J. Oyewumi, Foundations Phys. Lett. 18, 75 (2005) http://dx.doi.org/10.1007/s10702-005-2481-9[Crossref]
• [15] S.M. Ikhdair, R. Sever, J. Molec. Struct.-Theochem, doi:10.1016/j.theochem.2007.12.044 [Crossref]
• [16] C. Berkdemir, A. Berkdemir, J. Han, Chem. Phys. Lett. 417, 326 (2006) http://dx.doi.org/10.1016/j.cplett.2005.10.039[Crossref]
• [17] G.C. Maitland et al., Intermolcular forces (Oxford Univ. Press, Oxford, 1987)
• [18] M.L. Klein, J.A. Vemebles, Rare gas solids 1 (Academic Press, New York, 1976)
• [19] I.I. Goldman, V.D. Krivchenkov, Problems in quantum mechanics (Pergamon Press, New York, 1961)
• [20] Y. Weissman, J. Jortner, Phys. Lett. A 70, 177 (1979) http://dx.doi.org/10.1016/0375-9601(79)90197-X[Crossref]
• [21] M.L. Seze, Chem. Phys. 87, 431 (1984) http://dx.doi.org/10.1016/0301-0104(84)85123-X[Crossref]
• [22] M. Sato, J. Goodisman, Am. J. Phys. 53, 350 (1985) http://dx.doi.org/10.1119/1.14408[Crossref]
• [23] S. Erkoc, R. Sever, Phys. Rev. A 37, 2687 (1988) http://dx.doi.org/10.1103/PhysRevA.37.2687[Crossref]
• [24] J.I. Julian, J. Ting, J. Phys. B 11, 1 (1994)
• [25] J. Pliva, J. Mol. Spectrosc. 193, 7 (1999) http://dx.doi.org/10.1006/jmsp.1998.7741[Crossref]
• [26] S.M. Ikhdair, R. Sever, Z. Phys. C 56, 155 (1992) http://dx.doi.org/10.1007/BF01589718[Crossref]
• [27] S.M. Ikhdair, R. Sever, Z. Phys. C 58, 153 (1993) http://dx.doi.org/10.1007/BF01554088[Crossref]
• [28] S.M. Ikhdair, R. Sever, Z. Phys. D 28, 1 (1993) http://dx.doi.org/10.1007/BF01437449[Crossref]
• [29] S.M. Ikhdair, R. Sever, Hadronic J. 15, 389 (1992)
• [30] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 18, 4215 (2003) http://dx.doi.org/10.1142/S0217751X03015088[Crossref]
• [31] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 19, 1771 (2004) http://dx.doi.org/10.1142/S0217751X0401780X[Crossref]
• [32] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 20, 4035 (2005) http://dx.doi.org/10.1142/S0217751X05022275[Crossref]
• [33] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 20, 6509 (2005) http://dx.doi.org/10.1142/S0217751X05021294[Crossref]
• [34] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 2191 (2006) http://dx.doi.org/10.1142/S0217751X06031636[Crossref]
• [35] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 3989 (2006) http://dx.doi.org/10.1142/S0217751X06030953[Crossref]
• [36] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 6699 (2006) http://dx.doi.org/10.1142/S0217751X06034100[Crossref]
• [37] S.M. Ikhdair, R. Sever, arXiv:hep-ph/0504176, Int. J. Mod. Phys. E (in press)
• [38] H.E. Mentgomery, JR., N.A. Aquino, K.D. Sen, Int. J. Quantum Chem. 107, 798 (2007) http://dx.doi.org/10.1002/qua.21211[Crossref]
• [39] S.M. Ikhdair, R. Sever, Int. J. Mod. Phys. A 21, 6465 (2006) http://dx.doi.org/10.1142/S0217751X06034240[Crossref]
• [40] S.M. Ikhdair, R. Sever, J. Math. Chem. 41, 329 (2007) http://dx.doi.org/10.1007/s10910-006-9080-2[Crossref]
• [41] S.M. Ikhdair, R. Sever, J. Math. Chem. 41, 343 (2007) http://dx.doi.org/10.1007/s10910-007-9226-x[Crossref]
• [42] S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2007) http://dx.doi.org/10.1007/s10910-006-9115-8[Crossref]
• [43] S.M. Ikhdair, R. Sever, J. Mol. Struct. (Theochem) 809, 103 (2007) http://dx.doi.org/10.1016/j.theochem.2007.01.019[Crossref]
• [44] S.M. Ikhdair, R. Sever, Int. J. Theor. Phys. 46, 1643 (2007) http://dx.doi.org/10.1007/s10773-006-9317-7[Crossref]
• [45] S.M. Ikhdair, R. Sever, Ann. Phys. (Leipzig) 16, 218 (2007) http://dx.doi.org/10.1002/andp.200610232[Crossref]

Identifiers

DOI

10.2478/s11534-008-0060-y