Abstract.
In this work, the bound state problem of some diatomic molecules in the Tietz-Wei potential with varying shapes is correctly solved by means of path integrals. Explicit path integration leads to the radial Green’s function in closed form for three different shapes of this potential. In each case, the energy equation and the wave functions are obtained from the poles of the radial Green’s function and their residues, respectively. Our results prove the importance of the optimization parameter ch in the study of this potential which has been completely ignored by the authors of the papers cited below. In the limit \( c_{h}\rightarrow 0\), the energy spectrum and the corresponding wave functions for the radial Morse potential are recovered.
Similar content being viewed by others
References
T. Tietz, J. Chem. Phys. 38, 3036 (1963)
H. Wei, Phys. Rev. A 42, 2524 (1990)
G.A. Natanson, Phys. Rev. A 44, 3377 (1991)
J.A. Kunc, F.J. Gordillo-Vasquez, J. Phys. Chem. A 101, 1595 (1997)
F.J. Gordillo-Vasquez, J.A. Kunc, J. Mol. Struct. (Theochem) 425, 263 (1998)
M. Hamzavi, A.A. Rajabi, H. Hassanabadi, Mol. Phys. 110, 389 (2012)
M. Hamzavi, A.A. Rajabi, K.E. Thylwe, Int. J. Quantum Chem. 112, 2701 (2012)
C.L. Pekeris, Phys. Rev. 45, 98 (1934)
B.J. Falaye, K.J. Oyewumi, S.M. Ikhdair, M. Hamzavi, Phys. Scr. 89, 115204 (2014)
D. Mikulski, M. Molski, J. Konarski, K. Eder, J. Math. Chem. 52, 162 (2014)
B.J. Falaye, S.M. Ikhdair, M. Hamzavi, J. Math. Chem. 53, 1325 (2015)
B.J. Falaye, S.M. Ikhdair, M. Hamzavi, J. Theor. Appl. Phys. 9, 151 (2015)
H. Hassanabadi, B.H. Yazarloo, S. Zarrinkamar, M. Solaimani, Int. J. Quantum Chem. 112, 3706 (2012)
A. Khodja, A. Kadja, F. Benamira, L. Guechi, Indian J. Phys. 91, 1561 (2017)
D. Peak, A. Inomata, J. Math. Phys. 10, 1422 (1969)
A. Arai, J. Math. Anal. Appl. 158, 63 (1991)
A. Arai, J. Phys. A 34, 4281 (2001)
C.S. Jia, J.Y. Liu, P.Q. Wang, Phys. Lett. A 372, 4779 (2008)
R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976)
M.F. Manning, N. Rosen, Phys. Rev. 44, 953 (1933)
C. Grosche, J. Phys. A 38, 2947 (2005)
A. Khodja, F. Benamira, L. Guechi, J. Math. Phys. 91, 1561 (2017)
C. Grosche, Phys. Rev. Lett. 71, 1 (1993)
F. Benamira, L. Guechi, S. Mameri, M.A. Sadoun, J. Math. Phys. 48, 032102 (2007)
F. Benamira, L. Guechi, S. Mameri, M.A. Sadoun, J. Math. Phys. 51, 032301 (2010)
N. Rosen, P.M. Morse, Phys. Rev. 42, 210 (1932)
H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, 5th ed. (World Scientific, Singapore, 2009)
P.M. Morse, Phys. Rev. 34, 57 (1929)
L.D. Landau, E.M. Lifchitz, Quantum Mechanics (Pergamon, Oxford, 1958)
S. Flügge, Practical Quantum Mechanics (Springer Verlag, Berlin, 1974)
A. Khodja, F. Benamira, L. Guechi, Int. J. Quantum Chem. 117, 5 (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khodja, A., Kadja, A., Benamira, F. et al. Complete non-relativistic bound state solutions of the Tietz-Wei potential via the path integral approach. Eur. Phys. J. Plus 134, 57 (2019). https://doi.org/10.1140/epjp/i2019-12430-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2019-12430-8