Geometric approach to inverse scattering for hydrogen-like systems in a homogeneous magnetic field
Geometric approach to inverse scattering for hydrogen-like systems in a homogeneous magnetic field
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均匀磁场中类氢系统逆散射的几何方法
DOI：
10.1063/1.532261
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Silke Arians
中科院分区：
文献类型：
--
作者：
Silke Arians
我们考虑一个量子粒子在均匀磁场中的哈密顿量和三维空间中的标量势。对于给定的磁场，散射算符的高速极限唯一地决定了标量势，如果它是短距离的。此外，如果存在远程势，则需要对远程部分（远尾）的一些知识来定义修正的多拉德波算符和散射算符。同样，它的高速度极限唯一地决定了给定磁场的总标量势。我们将我们的结果推广到两个相互作用的带相反电荷的量子粒子的系统。
We consider the Hamiltonian of one quantum particle in a homogeneous magnetic field and a scalar potential in three space dimensions. For a given magnetic field the high velocity limit of the scattering operator uniquely determines the scalar potential if it is of short range. If, in addition, long-range potentials are present, some knowledge of (the far out tail of) the long-range part is needed to define a modified Dollard wave operator and a scattering operator. Again its high velocity limit uniquely determines the total scalar potential for a given magnetic field. We generalize our results to a system of two interacting quantum particles with opposite electric charges.