2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153776In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.11 pages, RevTeX, 1 figure, uses epsfig and amssymb, available as a preprint on http://www.pt.tu-clausthal.de/preprints/asi-tpa/010-96.ps.gzQuantum PhysicsDifferential GeometryHigh Energy Physics - Theorytext