论文标题
量子波的经典表征：Madelung-Bohm电位的苛性股和零之间的比较
Classical Characterization of quantum waves: Comparison between the caustic and the zeros of the Madelung-Bohm potential
论文作者
论文摘要
从几何学的角度来看，腐蚀性是对波函数的最古典描述，因为它的进化受汉密尔顿 - 雅各比方程的控制。另一方面，根据Madelung-de Broglie-Bohm方程，Madelung-Bohm电位的零零给出了Schrödinger方程解决方案的最古典描述。在这项工作中，我们比较了这些描述，并通过分析射线在苛性碱上的组织方式，我们发现具有折叠腐蚀性的波形是最经典的束，因为Madelung-Bohm潜在的零零与苛性碱巧合相吻合。对于另一种类型的梁，Madelung-Bohm电位通常在腐蚀性上截至零。我们已经验证了一维通风和皮尔西梁的这些结果，因此，灾难理论构成了灾难。最后，我们指出，在某些情况下，Madelung-Bohm电位的零与超震荡现象有关。
From a geometric perspective, the caustic is the most classical description of a wavefunction since its evolution is governed by the Hamilton-Jacobi equation. On the other hand, according to the Madelung-de Broglie-Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung-Bohm potential. In this work, we compare these descriptions and, by analyzing how the rays are organized over the caustic, we find that the wavefunctions with fold caustic are the most classical beams because the zeros of the Madelung-Bohm potential coincide with the caustic. For another type of beams, the Madelung-Bohm potential is in general distinct to zero over the caustic. We have verified these results for the one-dimensional Airy and Pearcey beams, which accordingly to the catastrophe theory, their caustics are stable. Finally, we remark that for certain cases, the zeros of the Madelung-Bohm potential are linked with the superoscillation phenomenon.
