论文标题
固定散射理论，价格为$ 1 $ - 体史塔克运营商，ii
Stationary scattering theory for $1$-body Stark operators, II
论文作者
论文摘要
我们研究并发展了一类具有短距离电位的单身史塔克汉密尔顿人（包括库仑电势）的固定散射理论，继续我们在[AIIS1，AIIS2]中的研究。经典的散射轨道是通过渐近正交矩参数参数的，并且在这些矩形中定义了（量子）散射矩阵的内核。我们表明，散射矩阵是一种经典的伪差异操作员，并计算其核的对角线处的领先顺序奇异性。我们的方法可以看作是用于研究一体schrödinger运算符的散射矩阵而没有外部潜力的散射矩阵的方法的适应。它比Kvitsinsky-Kostrykin [KK1]以前使用的更具标准方法更灵活，更有信息，用于计算恒定外场（Stark Case）的散射矩阵内核的领先顺序奇异性（The Stark Case）。我们的方法依赖于Sommerfeld的独特性导致空间，微局部分析以及经典的相空间结构。
We study and develop the stationary scattering theory for a class of one-body Stark Hamiltonians with short-range potentials, including the Coulomb potential, continuing our study in [AIIS1,AIIS2]. The classical scattering orbits are parabolas parametrized by asymptotic orthogonal momenta, and the kernel of the (quantum) scattering matrix at a fixed energy is defined in these momenta. We show that the scattering matrix is a classical type pseudodifferential operator and compute the leading order singularities at the diagonal of its kernel. Our approach can be viewed as an adaption of the method of Isozaki-Kitada [IK] used for studying the scattering matrix for one-body Schrödinger operators without an external potential. It is more flexible and more informative than the more standard method used previously by Kvitsinsky-Kostrykin [KK1] for computing the leading order singularities of the kernel of the scattering matrix in the case of a constant external field (the Stark case). Our approach relies on Sommerfeld's uniqueness result in Besov spaces, microlocal analysis as well as on classical phase space constructions.
