R. de la Madrid The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential (176K, Latex2e with additional style documents) ABSTRACT. The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential is constructed. The one-dimensional rectangular potential provides another opportunity to show that the rigged Hilbert space fully accounts for Dirac's bra-ket formalism. The analogy between Dirac's formalism and Fourier methods is pointed out.