Compton Scattering Equation
康普顿散射方程
In his explanation of the Compton scattering experiment, Arthur Compton treated the x-ray photons as particles and applied conservation of energy and conservation of momentum to the collision of a photon with a stationary electron. Using the Planck relationship and the relativistic energy expression, conservation of energy takes the form
在解释康普顿散射实验时，阿瑟·康普顿将X射线光子视为粒子，并将光子与静止电子的碰撞中的能量守恒和动量守恒应用于该碰撞。利用普朗克关系式和相对论能量表达式，能量守恒的形式为
Conservation of momentum requires
动量守恒要求
where p=E/c is used for the photon momentum. Squaring this equation using the scalar product gives
其中使用 p=E/c 表示光子的动量。用标量积对这个方程平方得到
Again using the Planck relationship and the relativistic energy expression:
再次利用普朗克关系和相对论能量表达式：
The energy conservation expression above can be squared to give
上述能量守恒表达式平方后可得到
These two forms can be equated to give
这两种形式可以相等以得到
which can be rearranged to
这可以重新排列为
and finally to the standard Compton formula:
最后得到标准的康普顿公式：
| Calculation
计算 | Compton scattering experiment
康普顿散射实验 |
References:
Compton
Blatt
Sec 4.6
索引参考：Compton Blatt 第4.6节
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HyperPhysics ***** 量子物理 | R Nave |
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