  Although quasi-Keplerian discs are among the most common astrophysical
structures, computation of secular angular momentum transport within them
routinely presents a considerable practical challenge. In this work, we
investigate the secular small-inclination dynamics of a razor-thin particle
disc as the continuum limit of a discrete Lagrange-Laplace secular perturbative
theory and explore the analogy between the ensuing secular evolution --
including non-local couplings of self-gravitating discs -- and quantum
mechanics. We find the 'quantum' Hamiltonian that describes the time evolution
of the system and demonstrate the existence of a conserved inner product. The
lowest-frequency normal modes are numerically approximated by performing a Wick
rotation on the equations of motion. These modes are used to quantify the
accuracy of a much simpler local-coupling model, revealing that it predicts the
shape of the normal modes to a high degree of accuracy, especially in narrow
annuli, even though it fails to predict their eigenfrequencies.
