Semiclassical scattering amplitude at the maximum of the potential
Semiclassical scattering amplitude at the maximum of the potential
复制标题
势能最大值处的半经典散射振幅
作者：
I. Alexandrova;J. Bony;T. Ramond
我们研究了薛定谔算符在临界能级的散射振幅，这是势的唯一非简并极大值。我们不假设最大值点是非共振的，并使用Bony，Fujiie，Ramond和Zerzeri的结果来分析捕获轨迹的贡献。我们证明了散射振幅的半经典展开式，并计算了它的首项。我们表明，它有不同的数量级在相空间的特定区域。我们还证明了在这种设置的预解式的上限和下限。
We study the scattering amplitude for Schrodinger operators at a critical energy level, which is a unique non- degenerate maximum of the potential. We do not assume that the maximum point is non-resonant and use results by Bony, Fujiie, Ramond and Zerzeri to analyze the contributions of the trapped trajectories. We prove a semiclassical expansion of the scattering amplitude and compute its leading term. We show that it has different orders of magnitude in specific regions of phase space. We also prove upper and lower bounds for the resolvent in this setting.