Abstract
A study is undertaken to derive the exact solutions of the Klein–Gordon with the Mie-type potential in the presence of the nonzero space component of a vector potential field. The wave functions and the energy spectrum are derived via the Laplace transformation method and by assuming equal scalar and time component of the vector potential. The Mie-type potential describes four different types of potential at the same time. The energy spectrum separately is obtained for each potential, and an estimation of the most general case is introduced.
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