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A contemporary physicist would be hard put to agree entirely with the authorof a 1959 textbook on quantum mechanics, who wrote: "A second simple,one-dimensional system, somewhat divorced from reality but illustrative of theprinciples of the theory, is a particle in a box with finite walls." Interestin this prototypic system has not diminished over the years, and is not likelyto do so in the near future, because it has now been wedded to reality and seenas a paradigm for quantum wells and other nanosystems. The treatment of thistopic in standard textbooks has changed little over the last few decades, andsuch changes as have come to our notice leave, in our opinion, much to bedesired. The purpose of this article is to enable, even encourage, otherteachers to give the finite square well the attention that it deserves; to thisend, the authors provide a tutorial review that is more instructive andcomprehensive than the accounts presented in numerous textbooks and dispensedin still more numerous online resources, but does not make any additionaldemands on the mathematical abilities of the student. Given the elementalnature of the topic, the authors claim no originality; with nothing more thanthe winnowing fork in their hands, they can only clear the threshing floor,gather the wheat into the barn, and let others decide whether or no the chaffshould be burnt with unquenchable fire.

The finite square well: whatever is worth teaching at all is worth teaching well