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Wave Equation of a Particle with the Exponential Hamiltonian in the Gravitational and Electromagnetic Field

This paper presents a unified view of the relativistic motion of a particle in the gravitational and electromagnetic field. Deliberationhas been carried out withinthe Dirac quantum mechanical theory by using exponential metrics. This theoretical concept brings us to an algebraic sixth-degree equation and solving the equation isa complex mathematical problem. In this paper, we show the solutionfor a basic state of the system and indicated quantum gravitational effects in the area of Planck dimensions.

relativistic motion, sixth-degree equation

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