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Ehrenfest's theorem in the infinite square well is up to now only manifestedindirectly. The manifestation of this theorem is first done in the finitesquare well, and then consider the infinite square well as the limit of thefinite well. For a direct manifestation, we need a more precise formula todescribe the degree of infiniteness of the divergent potential energy. We showthat the potential energy term term, which is the product of the potentialenergy and the energy eigenfunction, is a well defined function which can beexpressed in terms of Dirac delta functions. This means that the infinity inthis model is not that vague but has obtained a specification. This resultsthat expectation values can be calculated precisely and Ehrenfest's thereom canbe confirmed directly.

Direct manifestation of Ehrenfest's theorem in the infinite square well model