We prove that if a solution of the time-dependent Schrödinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schrödinger operator, we use the spectral theory of the Laplacian and complex analysis and obtain a characterization of the initial conditions that lead to a sharp decay at any time. We then adapt the real variable methods first introduced by Escauriaza, Kenig, Ponce and Vega to establish a general sharp result in the case of bounded potentials.

中文翻译：

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树上薛定ding方程解的唯一性

我们证明，如果具有势能的齐次树上的时间相关Schrödinger方程的解在两个不同的时间快速衰减，则该解是微不足道的。对于免费的Schrödinger算子，我们使用拉普拉斯算子的光谱理论和复杂的分析方法，并获得了导致随时衰减的初始条件的特征。然后，我们采用Escauriaza，Kenig，Ponce和Vega首次引入的实变量方法，以在势能有限的情况下建立总体清晰的结果。