量子力学中的广义散射理论

IF 1.1 Q3 PHYSICS, MULTIDISCIPLINARY
Huai-Yu Wang
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引用次数: 0

摘要

在量子力学教科书中,介绍了单粒子散射理论。本文提出了广义散射理论,该理论原则上可以应用于任意数目粒子的散射问题。在实验室框架下,导出了广义Lippmann-Schwinger散射方程。我们强调推导是严格的,即使对于处理无穷小。不允许进行分析延拓等人工操作。在散射前N个粒子为平面波,散射后N个粒子为新平面波的情况下,给出了粒子的跃迁幅度和跃迁概率,并给出了广义S矩阵。证明了N个粒子从一组平面波到另一组平面波的跃迁概率等于互反过程的跃迁概率。将广义理论应用于单粒子散射和双粒子散射两个例子。当应用于单粒子散射问题时,我们的广义形式退化为通常在文献中看到的形式。将广义理论应用于两粒子散射问题时,给出了两粒子碰撞跃迁概率的计算公式。结果表明,两个自由粒子散射的跃迁概率与互反过程的跃迁概率相同。统计力学中玻尔兹曼输运方程的推导需要这种跃迁概率和恒等式。我们还讨论了相同粒子的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A generalized scattering theory in quantum mechanics
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of particle. In laboratory frame, a generalized Lippmann-Schwinger scattering equation is derived. We emphasized that the derivation is rigorous, even for treating infinitesimals. No manual operation such as analytical continuation is allowed. In the case that before scattering N particles are plane waves and after the scattering they are new plane waves, the transition amplitude and transition probability are given and the generalized S matrix is presented. It is proved that the transition probability from a set of plane waves to a new set of plane waves of the N particles equal to that of the reciprocal process. The generalized theory is applied to the cases of one- and two-particle scattering as two examples. When applied to single-particle scattering problems, our generalized formalism degrades to that usually seen in the literature. When our generalized theory is applied to two-particle scattering problems, the formula of the transition probability of two-particle collision is given. It is shown that the transition probability of the scattering of two free particles is identical to that of the reciprocal process. This transition probability and the identity are needed in deriving Boltzmann transport equation in statistical mechanics. The case of identical particles is also discussed.
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来源期刊
Journal of Physics Communications
Journal of Physics Communications PHYSICS, MULTIDISCIPLINARY-
CiteScore
2.60
自引率
0.00%
发文量
114
审稿时长
10 weeks
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