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arXiv · gr-qc/0611144

N-body Gravity and the Schroedinger Equation

P. S. Farrugia·R. B. Mann·T. C. Scott
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Abstract

We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the H$_{2}^{+}$ molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.

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P. S. Farrugia, R. B. Mann, T. C. Scott. 2007-09-06. N-body Gravity and the Schroedinger Equation. https://doi.org/10.1088/0264-9381%2F24%2F18%2F006

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