N-body Gravity and the Schroedinger Equation

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.

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

References in corpus (14)

• Dilaton Gravity in Two Dimensions
• The $D\to 2$ Limit of General Relativity
• New Approach for the Electronic Energies of the Hydrogen Molecular Ion
• Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
• Conserved masses in GHS Einstein and string black holes
• Canonical reduction of two-dimensional gravity for Particle Dynamics
• Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity
• Chaos in a Relativistic 3-body Self-Gravitating System
• Gravitation and Cosmology in Generalized (1+1)-dimensional dilaton gravity
• Exact Solutions to the Motion of Two Charged Particles in Lineal Gravity
• Chaos in an Exact Relativistic 3-body Self-Gravitating System
• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
• Energy for N-Body Motion in Two Dimensional Gravity
• Perturbative Quantum Gravity Coupled to Particles in (1+1)-Dimensions

Cited by in corpus (1)

• One-Dimensional Relativistic Self-Gravitating Systems