The Self-Consistent Schrödinger Evolution of Self-Gravitating Disks

Quasi-Keplerian self-gravitating disks are one of the most ubiquitous objects in nature, and characterization of long-period angular momentum transfer within these systems constitutes a classic problem of dynamical astronomy. In this work, we investigate the small-inclination dynamics of a razor-thin particle disk as the continuum limit of Lagrange-Laplace secular perturbation theory, and explore the analogy between the secular evolution of self-gravitating disks and evolution entailed by the Schrödinger equation. Application of this formalism to the study of external perturbations and the gravitational rigidity of the disk are discussed.