N-body Gravity and the Schroedinger Equation

Details N-body Gravity and the Schroedinger Equation N-body Gravity and the Schroedinger Equation

2006-11-27

arxiv.org/abs/gr-qc/0611144v2

Class.Quant.Grav.24:4647-4660,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Latex, references added, typos corrected, final version that appears in CQG

Scientific paper

10.1088/0264-9381/24/18/006

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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