Solution of Coulomb Path Integral in Momentum Space

Details Solution of Coulomb Path Integral in Momentum Space Solution of Coulomb Path Integral in Momentum Space

1998-07-27

arxiv.org/abs/quant-ph/9807073v2

Phys.Lett. A252 (1999) 277-280

Physics

Quantum Physics

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://w

Scientific paper

10.1016/S0375-9601(99)00018-3

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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