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Solution of Coulomb Path Integral in Momentum Space

Hagen Kleinert
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Abstract

The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to give for the first time a negative answer to an old question of quantum mechanics in curved spaces raised in 1957 by DeWitt, whether the Hamiltonian of a particle in a curved space contains an additional term proportional to the curvature scalar $R$. We show that this would cause experimentally wrong level spacings in the hydrogen atom. Our solution also gives a first experimental confirmation of the correctness of the measure of integration in path integrals in curved space implied by a recently discovered nonholonomic mapping principle.

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Hagen Kleinert. 1999-02-02. Solution of Coulomb Path Integral in Momentum Space. https://doi.org/10.1016/s0375-9601(99)00018-3

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