康普顿散射是电子与电磁场相互作用中一种比较重要的物理现象，本文应用经典量子论和量子电动力学计算了光子被相对论性运动电子散射后的波长移动，选择一种波长的X射线作为例子，利用数值计算方法直观显示波长移动与电子初动量以及散射角的关系.并进一步讨论了出现相干散射、逆康普顿散射的原因，以及发生这些现象的必需条件.

Compton scattering is a significant physical phenomenon, arising from the interaction between electrons and the electromagnetic field. In this paper, the wavelength shift of photons scattered by relativistically moving electrons is calculated using classical quantum theory and quantum electrodynamics (QED). Taking X-rays of a specific wavelength as an example, this paper employs numerical methods to visually illustrate the dependence of  the wavelength shift on both the initial electron momentum and the scattering angle. Furthermore, this paper discusses the underlying mechanisms and necessary conditions for the occurrence of the interference scattering and inverse Compton scattering.