Classical characterization of quantum waves: comparison between the caustic and the zeros of the Madelung–Bohm potential

From a geometric perspective, the caustic is most classical description of wavefunction since its evolution governed by Hamilton-Jacobi equation. On other hand, according to Madelung-de Broglie-Bohm equations, solution Schr\"odinger equation given zeros Madelung-Bohm potential. In this work, we compare these descriptions and, analyzing how rays are organized over caustic, find that wavefunctions with fold beams because potential coincide caustic. For another type beams, in general distinct zero We have verified results for one-dimensional Airy and Pearcey which accordingly catastrophe theory, their caustics stable. Finally, remark certain cases, linked superoscillation phenomenon.