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From a geometric perspective, the caustic is the most classical descriptionof a wavefunction since its evolution is governed by the Hamilton-Jacobiequation. On the other hand, according to the Madelung-de Broglie-Bohmequations, the most classical description of a solution to the Schr\"odingerequation is given by the zeros of the Madelung-Bohm potential. In this work, wecompare these descriptions and, by analyzing how the rays are organized overthe caustic, we find that the wavefunctions with fold caustic are the mostclassical beams because the zeros of the Madelung-Bohm potential coincide withthe caustic. For another type of beams, the Madelung-Bohm potential is ingeneral distinct to zero over the caustic. We have verified these results forthe one-dimensional Airy and Pearcey beams, which accordingly to thecatastrophe theory, their caustics are stable. Finally, we remark that forcertain cases, the zeros of the Madelung-Bohm potential are linked with thesuperoscillation phenomenon.

Classical Characterization of quantum waves: Comparison between the caustic and the zeros of the Madelung-Bohm potential