N-body Gravity and the Schroedinger Equation

TL;DR

This paper explores the dynamics of N-body gravitational systems in two dimensions, mapping them onto quantum mechanical problems, and provides algorithms for solving these systems, extending to charged bodies.

Contribution

It introduces a novel mapping of 2D gravitational N-body problems to quantum mechanics and develops a general algorithm for their solution, including charged bodies.

Findings

Mapping of gravitational N-body systems to quantum problems

Reduction of the problem to known 2- and 3-body cases

Extension to include electromagnetic charges

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.