Dong, Shihai; Sun, Guohua The series solutions of the non-relativistic equation with the Morse potential. (English) Zbl 1073.81557 Phys. Lett., A 314, No. 4, 261-266 (2003). Summary: In this Letter the analytical solutions of the two-dimensional Schrödinger equation with the Morse potential are obtained by the series expansion method. We then generalize this method to the \(D\)-dimensional Schrödinger equation case. The studied Morse potential itself is expanded in the series about the origin. Cited in 14 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q40 PDEs in connection with quantum mechanics Keywords:two-dimensional Schrödinger equation; \(D\)-dimensional Schrödinger equation PDFBibTeX XMLCite \textit{S. Dong} and \textit{G. Sun}, Phys. Lett., A 314, No. 4, 261--266 (2003; Zbl 1073.81557) Full Text: DOI References: [1] Schiff, L. I., Quantum Mechanics (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0068.40202 [2] Dirac, P. A., The Principles of Quantum Mechanics (1958), Oxford Univ. Press · Zbl 0080.22005 [3] Landau, L. D.; Lifshitz, E. M., Quantum Mechanics, Non-Relativistic Theory (1977), Pergamon · Zbl 0178.57901 [4] Jensen, P., Mol. Phys., 98, 1253 (2000) [5] Child, M. S.; Halonen, L., Adv. Chem. Phys., 62, 1 (1984) [6] Pauling, L.; Wilson, E. B., Introduction to Quantum Mechanics with Applications to Chemistry (1985), Dover: Dover New York [7] Mörse, P. M., Phys. Rev., 34, 57 (1929) [8] Dabrowska, J. W.; Khare, A.; Sukhatme, U. P., J. Phys. A: Math. Gen., 21, L195 (1988) [9] Balentekin, A. B., Phys. Rev. A, 57, 4188 (1998) [10] Dong, S. H.; Lemus, R.; Frank, A., Int. J. Quantum Chem., 86, 433 (2002), and references therein [11] Fernández, F.; Castro, A., Algebraic Methods in Quantum Chemistry and Physics. Algebraic Methods in Quantum Chemistry and Physics, Mathematical Chemistry Series (1996), CRC Press · Zbl 0862.46046 [12] Lévai, G., J. Phys. A: Math. Gen., 27, 3809 (1994) · Zbl 0841.34088 [13] Benedict, M. G.; Molnár, B., Phys. Rev. A, 60, R1737 (1999) [14] Chetouani, L.; Guechi, L.; Hammann, T. F., Czech. J. Phys., 43, 13 (1993) [15] Flügge, S.; Walger, P.; Weiguni, A., J. Mol. Spectrosc., 23, 243 (1967) [16] Talukdar, B.; Chatterji, M.; Banerjee, P., Pramana, 13, 15 (1979) [17] Rouse, C. A., Phys. Rev. A, 36, 1 (1987) [18] Erdelyi, A., Higher Transcendental Functions, Vol. 2 (1953), McGraw-Hill: McGraw-Hill New York, p. 232 [19] Chatterjee, A., Phys. Rep., 186, 249 (1990) [20] Dong, S. H., Found. Phys. Lett., 15, 385 (2002) [21] Dong, S. H., J. Phys. A: Math. Gen., 36, 4977 (2003) [22] S.H. Dong, X.Y. Gu, Z.Q. Ma, Int. J. Mod. Phys. E, in press; S.H. Dong, X.Y. Gu, Z.Q. Ma, Int. J. Mod. Phys. E, in press This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.