# 電磁輻射

(重新導向自 电磁波)

## 概念

### 波動模型

${\displaystyle v=\nu \lambda \,\!}$

${\displaystyle u={\frac {1}{2\mu _{0}}}B^{2}+{\frac {\epsilon _{0}}{2}}E^{2}\,\!}$

### 粒子模型和量子理論

${\displaystyle E=h\nu \,\!}$

${\displaystyle p={\frac {E}{c}}={\frac {h\nu }{c}}={\frac {h}{\lambda }}\,\!}$

### 傳播速度

${\displaystyle E=h\nu \,\!}$

${\displaystyle n=c/v\,\!}$

## 熱輻射

${\displaystyle {U \over V}={\frac {8\pi ^{5}(kT)^{4}}{15(hc)^{3}}}\,\!}$

${\displaystyle C_{V}={\frac {32\pi ^{5}k^{4}T^{3}}{15(hc)^{3}}}\,\!}$

## 從電磁理論推導

${\displaystyle \nabla \cdot \mathbf {E} =0\,\!}$（1）
${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}$（2）
${\displaystyle \nabla \cdot \mathbf {B} =0\,\!}$（3）
${\displaystyle \nabla \times \mathbf {B} =\mu _{0}\epsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\,\!}$（4）

${\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)\,\!}$（5）

${\displaystyle \nabla \times \left(\nabla \times \mathbf {E} \right)=\nabla \left(\nabla \cdot \mathbf {E} \right)-\nabla ^{2}\mathbf {E} =-\nabla ^{2}\mathbf {E} \,\!}$（6）

${\displaystyle \nabla \times \left(-{\frac {\partial \mathbf {B} }{\partial t}}\right)=-{\frac {\partial }{\partial t}}\left(\nabla \times \mathbf {B} \right)=-\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}\,\!}$（7）

 ${\displaystyle \nabla ^{2}\mathbf {E} =\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {E} }{\partial t^{2}}}\,\!}$。

 ${\displaystyle \nabla ^{2}\mathbf {B} =\mu _{0}\epsilon _{0}{\frac {\partial ^{2}\mathbf {B} }{\partial t^{2}}}\,\!}$。

${\displaystyle \Box \mathbf {E} =0\,\!}$
${\displaystyle \Box \mathbf {B} =0\,\!}$

${\displaystyle \mathbf {E} =\mathbf {E} _{0}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)\,\!}$

${\displaystyle \nabla ^{2}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)={\frac {1}{{c_{0}}^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}f\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)\,\!}$

${\displaystyle \nabla \cdot \mathbf {E} =\mathbf {k} \cdot \mathbf {E} _{0}f'\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)=0\,\!}$

${\displaystyle \mathbf {E} \cdot \mathbf {k} =0\,\!}$

${\displaystyle \nabla \times \mathbf {E} ={\hat {\mathbf {k} }}\times \mathbf {E} _{0}f'\left(\mathbf {k} \cdot \mathbf {r} -\omega t\right)=-{\frac {\partial \mathbf {B} }{\partial t}}\,\!}$

${\displaystyle \mathbf {B} ={\frac {1}{\omega }}\mathbf {k} \times \mathbf {E} \,\!}$

## 參考文獻

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14. ^ French, Anthony, An Introduction to Quantum Physics, W. W. Norton, Inc., 1978
15. ^ （英文）國際純粹與應用化學聯合會．"photoionization"．《化學術語總目錄》在線版．
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17. ^ Griffiths, David J., Hyperfine splitting in the ground state of hydrogen (PDF), American Journal of Physics, August 1982, 50 (8): pp. 698