Exact treatment of the relativistic double ring-shaped Kratzer potential using the quantum Hamilton–Jacobi formalism

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We study the Klein–Gordon equation with noncentral and separable potential under the condition of equal scalar and vector potentials and we obtain the corresponding relativistic quantum Hamilton–Jacobi equation. The application of the quantum Hamilton–Jacobi formalism to the double ring-shaped Kratzer potential leads to its relativistic energy spectrum as well as the corresponding eigenfunctions.