The one‐dimensional square quantum well of varying width is shown to be an instructive example for testing the appropriateness of approximate solutions in quantum mechanics. The range of wall speeds over which the adiabatic approximation is applicable is investigated and related to the initial energy of the quantum system for both expanding and contracting wells. However, of more interest is the applicability of the sudden approximation to these systems. It is shown that this approximation is appropriate for expanding wells at quite modest wall speeds, whereas the approximation cannot be applied for contracting wells no matter how rapidly the well width contracts. The physical reasons for the inapplicability of the sudden approximation for contracting wells is investigated.