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Shrodinger Equation in General Relativity

Hans J. Wospakrik

Abstract. Schrodinger equation in GR for a charged particle in Coulomb potential is presented, derived from the formulation of Klein-Gordon equation in GR with an assumption that the kinetic and potential energy are small in comparison with the rest energy mc2. The term Newtonian, potential appeared directly as expected from the non-relativistic Schrodinger equation in the Newtonian gravitational field. It is shown that its radial equation posseses a non-essential singular point at r = 0, therefore it has a power series solution about r = 0. Perturbation theory is used to find its approximation solution, encountered some divergences that remained unsolved.


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