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D-dimensional energies for scandium monoiodide

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Abstract

We solve the Schrödinger equation with the Morse potential energy model in \(D\) spatial dimensions. The bound state rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For a fixed vibrational quantum number and various rotational quantum numbers, the energies for the \(\hbox {X}^{1}\Sigma ^{+}\) state of ScI molecule increase as \(D\) increases. We observe that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. The dimensional scaling method resembles a translation transformation from the higher dimensions to the actual three dimensions.

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Acknowledgments

We would like to thank the kind referees for their helpful comments and suggestions which have greatly improved the manuscript. This work was supported by the National Natural Science Foundation of China under Grant No. 10675097, and the Science Foundation of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation of China under Grant No. PLN-ZL001.

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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Jian-Fen Du, Ping Guo & Chun-Sheng Jia

  2. School of Petroleum Engineering, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Jian-Fen Du

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  1. Jian-Fen Du
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  2. Ping Guo
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  3. Chun-Sheng Jia
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Correspondence to Chun-Sheng Jia.

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Du, JF., Guo, P. & Jia, CS. D-dimensional energies for scandium monoiodide. J Math Chem 52, 2559–2569 (2014). https://doi.org/10.1007/s10910-014-0399-9

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