定态散射态的叠加积分
Overlap integral of stationary scattering states
AI总结：
本文研究有限宽度势中散射态的叠加积分，发现非对角项导致定态叠加具有时变范数和有限概率流，而在特殊势和自由理论中非对角项消失，不同能量态叠加可精确描述孤立粒子的散射过程。
摘要：
有限宽度势中散射态的叠加积分通过其渐近行为表示，能量 $E_1$ 和 $E_2$ 的部分由正比于 $δ(E_1-E_2)$ 的对角项和非对角项组成。由于非对角项的存在，定态的叠加具有随时间变化的范数和有限的概率流。这些并不代表孤立态。在各种特殊势和自由理论中，非对角项不存在，不同能量态的叠加代表孤立粒子，能够精确描述散射过程。
英文摘要：
The overlap integrals of scattering states in potentials of finite widths are expressed with their asymptotic behaviors and those of energies $E_1$ and $E_2$ consist of diagonal terms that are proportional to $δ(E_1-E_2)$ and nondiagonal terms. Owing to the composition of nondiagonal terms, superpositions of stationary states have time-dependent norms and finite probability currents. These do not represent isolate states. In various exceptional potentials and in free theory, nondiagonal terms do not exist, and the superpositions of states with different energies represent isolate particles that exactly describe scattering processes.
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