2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194295We 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.15 pages, Latex, references added, typos corrected, final version that appears in CQGGeneral Relativity and Quantum Cosmologytext