Feynman Perturbation Series for the Morse Potential
Affiliation(s)
1Département de Mathématiques, Faculté des Sciences exactes et Informatique, Université Med Saddik Ben Yahia, Jijel, Algérie 2Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah. Ouargla, Algérie. Département de Physique, Faculté des Sciences et des Sciences de l’Ingénieur, Laboratoire LRPPS Université Kasdi Merbah, Ouargla, Algérie. Département de Physique, Université de Constantine I, Constantine, Algérie.
1Département de Mathématiques, Faculté des Sciences exactes et Informatique, Université Med Saddik Ben Yahia, Jijel, Algérie 2Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah. Ouargla, Algérie. Département de Physique, Faculté des Sciences et des Sciences de l’Ingénieur, Laboratoire LRPPS Université Kasdi Merbah, Ouargla, Algérie. Département de Physique, Université de Constantine I, Constantine, Algérie.
ABSTRACT
In this paper we give an alternative treatment of the Schrodinger equation with the Morse potential, which based on the exact summation of the Feynman perturbation series in its original form. Using Fourier transform we establish a recurrence equation between terms of the perturbation series. Finally, by the inverse Fourier transform and some technical tools of the ordinary differential equations of the second order, we can compute the exact sum of the perturbation series which is the Green’s function of the problem.
KEYWORDS
Morse Potential; Green’s Function; Propagator; Path Integral; Perturbation Series; Fourier Transform
Morse Potential; Green’s Function; Propagator; Path Integral; Perturbation Series; Fourier Transform
Cite this paper
Badredine, B. , Tayeb, M. and Lyazid, C. (2014) Feynman Perturbation Series for the Morse Potential. Journal of Modern Physics, 5, 177-185. doi: 10.4236/jmp.2014.55028.
Badredine, B. , Tayeb, M. and Lyazid, C. (2014) Feynman Perturbation Series for the Morse Potential. Journal of Modern Physics, 5, 177-185. doi: 10.4236/jmp.2014.55028.
References
[1] Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path-Integral. McGraw-Hill, New York. [2] Goovaerts, M.J., Babcenco, A. and Devreese, J.T. (1973) Journal of Mathematical Physics, 14, 554.
http://dx.doi.org/10.1063/1.1666355 [3] Lawande, S.V. and Bhagwat, K.V. (1988) Physics Letters A, 131, 8-10.
http://dx.doi.org/10.1016/0375-9601(88)90622-6 [4] Grosche, C. (1990) Journal of Physics A: Mathematical and General, 23, 5205-5234.
http://dx.doi.org/10.1088/0305-4470/23/22/013 [5] Bhagwat, K.V. and Lawande, S.V. (1989) Physics Letters A, 135, 417.
http://dx.doi.org/10.1016/0375-9601(89)90038-8 [6] Lin, D.H. (1997) Journal of Physics A: Mathematical and General, 30, 4365.
http://dx.doi.org/10.1088/0305-4470/30/12/022 [7] Lin, D.H. (1998) Journal of Physics A: Mathematical and General, 31, 7577.
http://dx.doi.org/10.1088/0305-4470/31/37/015 [8] Bhagwat, K.V. and Lawande, S.V. (1989) Physics Letters A, 141, 321.
http://dx.doi.org/10.1016/0375-9601(89)90057-1 [9] Acila, M., Benali, B. and Meftah, M.T. (2006) Journal of Physics A: Mathematical and General, 39, 1357-1366.
http://dx.doi.org/10.1088/0305-4470/39/6/009 [10] Landau, L. and Lifchitz, E. (1974) Quantum Mechanics. Vol. III, Edition Mir, Moscou. [11] Khandekar, D.C. and Lawande, S.V. (1986) Physics Reports (Review Section of Physics Letters), 137, 115-229.
http://dx.doi.org/10.1016/0370-1573(86)90029-3 [12] Duru, I.H. (1983) Physical Review D, 28, 2689-2692. http://dx.doi.org/10.1103/PhysRevD.28.2689 [13] Fischer, W., Leschke, H. and Muller, P. (1992) Journal of Physics A: Mathematical and General, 25, 3835-3853.
http://dx.doi.org/10.1088/0305-4470/25/13/029 [14] Soylu, A., Bayrak, O. and Boztosun, I. (2012) Central European Journal of Physics, 10, 953-959.
http://dx.doi.org/10.2478/s11534-012-0018-y [15] Barakat, T., Abodayeh, K. and Al-dossary, O.M. (2006) Czechoslovak Journal of Physics, 56, 583-590.
http://dx.doi.org/10.1007/s10582-006-0122-6 [16] Addis, B. and Schachinger, W. (2010) Computational Optimization and Applications, 47, 129-131.
http://dx.doi.org/10.1007/s10589-008-9205-6 [17] Popov, V.N. (2013) High Temperature, 51, 66-71. http://dx.doi.org/10.1134/S0018151X13010124 [18] Foldi, P., Benedict, M.G. and Czéryak, A. (2004) Acta Physica Hungarica Series B, Quantum Electronics, 20, 25-28. [19] Boudjedaa, B., Meftah, M.T. and Chetouani, L. (2007) Turkish Journal of Physics, 31, 197-203.
[1] Feynman, R.P. and Hibbs, A.R. (1965) Quantum Mechanics and Path-Integral. McGraw-Hill, New York. [2] Goovaerts, M.J., Babcenco, A. and Devreese, J.T. (1973) Journal of Mathematical Physics, 14, 554.
http://dx.doi.org/10.1063/1.1666355 [3] Lawande, S.V. and Bhagwat, K.V. (1988) Physics Letters A, 131, 8-10.
http://dx.doi.org/10.1016/0375-9601(88)90622-6 [4] Grosche, C. (1990) Journal of Physics A: Mathematical and General, 23, 5205-5234.
http://dx.doi.org/10.1088/0305-4470/23/22/013 [5] Bhagwat, K.V. and Lawande, S.V. (1989) Physics Letters A, 135, 417.
http://dx.doi.org/10.1016/0375-9601(89)90038-8 [6] Lin, D.H. (1997) Journal of Physics A: Mathematical and General, 30, 4365.
http://dx.doi.org/10.1088/0305-4470/30/12/022 [7] Lin, D.H. (1998) Journal of Physics A: Mathematical and General, 31, 7577.
http://dx.doi.org/10.1088/0305-4470/31/37/015 [8] Bhagwat, K.V. and Lawande, S.V. (1989) Physics Letters A, 141, 321.
http://dx.doi.org/10.1016/0375-9601(89)90057-1 [9] Acila, M., Benali, B. and Meftah, M.T. (2006) Journal of Physics A: Mathematical and General, 39, 1357-1366.
http://dx.doi.org/10.1088/0305-4470/39/6/009 [10] Landau, L. and Lifchitz, E. (1974) Quantum Mechanics. Vol. III, Edition Mir, Moscou. [11] Khandekar, D.C. and Lawande, S.V. (1986) Physics Reports (Review Section of Physics Letters), 137, 115-229.
http://dx.doi.org/10.1016/0370-1573(86)90029-3 [12] Duru, I.H. (1983) Physical Review D, 28, 2689-2692. http://dx.doi.org/10.1103/PhysRevD.28.2689 [13] Fischer, W., Leschke, H. and Muller, P. (1992) Journal of Physics A: Mathematical and General, 25, 3835-3853.
http://dx.doi.org/10.1088/0305-4470/25/13/029 [14] Soylu, A., Bayrak, O. and Boztosun, I. (2012) Central European Journal of Physics, 10, 953-959.
http://dx.doi.org/10.2478/s11534-012-0018-y [15] Barakat, T., Abodayeh, K. and Al-dossary, O.M. (2006) Czechoslovak Journal of Physics, 56, 583-590.
http://dx.doi.org/10.1007/s10582-006-0122-6 [16] Addis, B. and Schachinger, W. (2010) Computational Optimization and Applications, 47, 129-131.
http://dx.doi.org/10.1007/s10589-008-9205-6 [17] Popov, V.N. (2013) High Temperature, 51, 66-71. http://dx.doi.org/10.1134/S0018151X13010124 [18] Foldi, P., Benedict, M.G. and Czéryak, A. (2004) Acta Physica Hungarica Series B, Quantum Electronics, 20, 25-28. [19] Boudjedaa, B., Meftah, M.T. and Chetouani, L. (2007) Turkish Journal of Physics, 31, 197-203.