2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92500We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By generalizing to the unit disk the idea of turns, introduced by Hamilton to represent rotations on the sphere, we develop a method to represent transfer matrices by hyperbolic turns, which can be composed by a simple parallelogramlike rule.8 pages, 5 figures. This paper is dedicated to Alberto Galindo the occasion of his seventieth birthday. Submitted for publicationQuantum PhysicsPhysics Educationtext