标题： 两粒子态和多通道散射中的$S$-矩阵元 显示英文标题

标题： Two Particle States and the $S$-matrix Elements in Multi-channel Scattering

摘要： 使用量子力学模型，在所有三个方向上具有周期性边界条件的立方箱中研究了两粒子两通道散射的精确能量本征态。 得到了箱中精确能量本征值与连续谱中两通道$S$矩阵元之间的关系。 这一结果可以看作是众所周知的卢舍尔公式（Lüscher's formula）的推广，该公式在弹性散射中建立了类似的关系。 显示英文摘要

摘要： Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.