Abstract
Abstract The Klein-Gordon equation in the cosmic string and rainbow gravity spacetime under the influence of an external magnetic field and Coulomb potential for PDM particles is investigated using the NU method. From solution of the Klein-Gordon system with PDM particles, the energy levels are obtained. The energy levels are numerically calculated as a function of rainbow gravity parameters, as a function of magnetic field parameters, as a function of position-dependent mass parameters. We apply some rainbow functions and the results show that the negative and positive energy levels for rainbow function 1 are symmetrical compared to rainbow function 2.
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