N-body gravity and the Schrödinger equation

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.