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Exact Solutions of the Klein–Gordon Equation with Position-Dependent Mass for Mixed Vector and Scalar Kink-Like Potentials

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Abstract

The relativistic problem of spinless particles with position-dependent mass subject to kink-like potentials (~tanh αx) is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Klein–Gordon equation with the vector and scalar kink-like potential coupling, and obtain the bound state solutions in the closed form. It is found that in the presence of position-dependent mass there exists the symmetry that the discrete positive energy spectra and negative energy spectra are symmetric about zero energy for the case of a mixed vector and scalar kink-like potential coupling, and in the presence of constant mass this symmetry only appears for the cases of a pure scalar kink-like potential coupling or massless particles.

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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

    Chun-Sheng Jia, Xiao-Ping Li & Lie-Hui Zhang

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  1. Chun-Sheng Jia
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  2. Xiao-Ping Li
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  3. Lie-Hui Zhang
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Correspondence to Chun-Sheng Jia.

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Jia, CS., Li, XP. & Zhang, LH. Exact Solutions of the Klein–Gordon Equation with Position-Dependent Mass for Mixed Vector and Scalar Kink-Like Potentials. Few-Body Syst 52, 11–18 (2012). https://doi.org/10.1007/s00601-011-0258-1

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