We consider the evolution, for a time-dependent Schrödinger equation, of the so-called Dirac comb. We show how this evolution allows us to recover explicitly (indeed optically) the values of the quadratic generalized Gauss sums. Moreover we use the phenomenon of superoscillatory sequences to prove that such Gauss sums can be asymptotically recovered from the values of the spectrum of any sufficiently regular function compactly supported on $\mathbb{R}$. The fundamental tool we use is the so called Galilean transform that was introduced and studied in the context on non-linear time dependent Schrödinger equations. Furthermore, we utilize this tool to understand in detail the evolution of an exponential $e^{i\omega x}$ in the case of a Schrödinger equation with time-independent periodic potential.

对于随时间变化的薛定ding方程，我们考虑了所谓的狄拉克梳子的演化。我们展示了这种进化如何使我们能够明确地（实际上是光学地）恢复二次广义高斯和的值。此外，我们使用超振荡序列现象来证明，可以从紧紧支持在其上的任何足够规则函数的频谱值渐近地恢复此类高斯和。$\mathbb{[R}$。我们使用的基本工具是所谓的Galilean变换，它是在非线性时间相关Schrödinger方程的背景下引入和研究的。此外，我们利用此工具来详细了解指数的演变${Ë}^{\mathrm{一世}\omega X}$ 在具有与时间无关的周期性电势的Schrödinger方程中。