The inverse problem in potential wells

We study the solution of the inverse spectral problem of a potential well ( PW). This problem constitutes a good exercise for the understanding of the Schrodinger equation, especially if we take into account that often this to pic is not undertaken in regular courses of Quantum Mechanics. This exercis e also propitiates the training of the students in the solution of this kin d of problems, which frequently appears in research experimental work. We t hink that the exercises that are demonstrated in this paper could be includ ed in Quantum Mechanics regular courses. The inverse problem presented here consists in the reconstruction of a PW, i.e., find the height of the barri er and the width of the well, provided the values of the discrete energy le vels or the transition energies between them are known. We show three diffe rent cases of this problem referred to rectangular PWs. In all cases, the e quations are deduced and the developed method is illustrated graphically.