康普顿效应中散射电子的德布罗意波长和频率
de Broglie Wavelength and Frequency of the Scattered Electrons in Compton Effect
摘要：
现代物理本科课程一般考虑康普顿效应的粒子解释。受一个学生在现代物理本科考试中的解答的启发，我们考虑了反冲电子在康普顿效应中的波动特性。散射电子的德布罗意波长、波和时钟频率分别用入射光子和散射光子的波长和频率表示，使用熟悉的康普顿效应的粒子解释，其中最初电子是静止的，其自旋被忽略。非相对论和相对论的情况下被认为是。计算了入射光子能量与反冲电子散射角的函数关系下，散射电子的德布罗意波长、波和钟频率的数值，并考虑了相对论效应对反冲电子的德布罗意波长的影响。所获得的最小值在X射线的范围内。忽略电子的静止质量而得到的非相对论性德布罗意波频率导致其值的低估。德布罗意波长和时钟频率的康普顿散射实验的影响进行了简要讨论，并指出可能的扩展所获得的数学公式。这些结果对于理解康普顿效应中反冲电子的波粒二象性是有用的。
英文摘要：
The undergraduate courses on modern physics generally consider the particle interpretation of Compton effect. Motivated by a student's solution in an undergraduate examination on modern physics here we consider the wave characteristics of recoiled electrons in the Compton effect. The de Broglie wavelength, wave and clock frequency of the scattered electrons are expressed in terms of the wavelength and the frequency of the incident and the scattered photons respectively using the familiar particle interpretation of the Compton effect, where initially the electron is at rest and its spin is ignored. Both non-relativistic and relativistic cases are considered. Numerical values of de Broglie wavelength, wave and clock frequency of the scattered electron are calculated for an incident photon energy that was used in the original experiment of Compton as a function of the scattering angle of the recoiled electron. Considering the relativistic effects which are however insignificant for the de Broglie wavelength of the recoiled electron under these conditions, the minimum value obtained is in the range of X-rays. The non-relativistic de Broglie wave frequency obtained by neglecting the rest mass of the electron leads to an underestimation of its value. The implications of de Broglie wavelength and clock frequency for Compton scattering experiments are briefly discussed and possible extensions of the obtained mathematical formulations are indicated. The results are useful for understanding the wave-particle duality of the recoiled electron in the context of the Compton effect.
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