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Solutions of the Klein–Gordon equation with the improved Tietz potential energy model

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Abstract

We present the relativistic rotation–vibrational energy equation of a diatomic molecule which moves under the improved Tietz potential energy model in higher spatial dimensions. The nonrelativistic limits of the bound state solutions of the Klein–Gordon equation are the bound state solutions of the Schrödinger equation with the same potential energy function. Numerical analysis results show that there exists a critical point around which the solution behaviors bifurcate into two extreme cases. Below the critical point, the behavior of the relativistic vibrational energies for the ground electronic state of carbon monoxide in higher dimensions keeps similar to that of the three-dimensional system, while this symmetry phenomenon breaks and the Klein–Gordon equation has no stability solution upon the critical point.

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Acknowledgements

We would like to thank the kind referees for positive and invaluable suggestions which have greatly improved the manuscript. This work was supported by the Key Program of National Natural Science Foundation of China under Grant No. 51534006.

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Authors and Affiliations

  1. Experimental School Affiliated to Xindu No.1 Middle School, Chengdu, 610500, People’s Republic of China

    Han-Bin Liu

  2. Sichuan Police College, Luzhou, 646000, Sichuan, People’s Republic of China

    Liang-Zhong Yi

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

    Chun-Sheng Jia

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  1. Han-Bin Liu
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Correspondence to Chun-Sheng Jia.

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Liu, HB., Yi, LZ. & Jia, CS. Solutions of the Klein–Gordon equation with the improved Tietz potential energy model. J Math Chem 56, 2982–2994 (2018). https://doi.org/10.1007/s10910-018-0927-0

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  • DOI: https://doi.org/10.1007/s10910-018-0927-0

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