Remarks concerning the solution of the equations of quantum geometrodynamics by successive approximations

Mathematics – Probability

Scientific paper

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Approximation, Einstein Equations, Gravitation Theory, Quantum Theory, Relativity, Schroedinger Equation, Bundles, Eigenvalues, Error Functions, Gravitational Fields, Potential Theory, Probability Distribution Functions

Scientific paper

The improved version of the Einstein-Schroedinger equation of quantum gravity found by Christodoulou (1972) is solved in the linear approximation. The solution differs from that obtained by Kuchar (1970) for the original version of the equation by an additional quantum effect. The energy, as deduced from measurements of the gravitational potential at infinity, has an error-function probability distribution about its eigenvalue. The higher approximations are also considered, and the appearance of a third quantum number, possibly related to the transition matrix, is deduced.

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