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We consider the electron dynamics and transport properties of one-dimensional continuous models with random, short-range correlated impurities. We develop a generalized Poincaré map formalism to cast the Schrödinger equation for any potential into a discrete set of equations, illustrating its application by means of a specific example. We then concentrate on the case of a Kronig-Penney model with dimer impurities. The previous technique allows us to show that this model presents infinitely many resonances (zeroes of the reflection coefficient at a single dimer) that give rise to a band of extended states, in contradiction with the general viewpoint that all one-dimensional models with random potentials support only localized states. We report on exact transfer-matrix numerical calculations of the transmission coefficient, density of states, and localization length for various strengths of disorder. The most important …