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# 德鲁德模型

## 维基百科，自由的百科全书

${\displaystyle {\frac {d}{dt))\mathbf {p} (t)=q\mathbf {E} -{\frac {\mathbf {p} (t)}{\tau )),}$

${\displaystyle \mathbf {J} =\left({\frac {nq^{2}\tau }{m))\right)\mathbf {E} .}$

## 解释

### 直流电场

${\displaystyle d\langle \mathbf {p} \rangle =q\mathbf {E} \tau .}$

${\displaystyle \langle \mathbf {p} \rangle =q\mathbf {E} \tau .}$

${\displaystyle \langle \mathbf {p} \rangle =m\langle \mathbf {v} \rangle ,}$
${\displaystyle \mathbf {J} =nq\langle \mathbf {v} \rangle ,}$

${\displaystyle \mathbf {J} =\left({\frac {nq^{2}\tau }{m))\right)\mathbf {E} .}$

### 时变分析

${\displaystyle \langle \mathbf {p} (t_{0}+dt)\rangle =\left(1-{\frac {dt}{\tau ))\right)\left(\langle \mathbf {p} (t_{0})\rangle +q\mathbf {E} dt+...\right),}$

${\displaystyle {\frac {d}{dt))\langle \mathbf {p} (t)\rangle =q\mathbf {E} -{\frac {\langle \mathbf {p} (t)\rangle }{\tau )),}$

${\displaystyle \langle \mathbf {p} (t)\rangle =q\tau \mathbf {E} +\mathbf {C} e^{-t/\tau ))$

${\displaystyle \langle \mathbf {p} \rangle =q\tau \mathbf {E} ,}$

${\displaystyle \langle \mathbf {p} \rangle =m\langle \mathbf {v} \rangle ,}$
${\displaystyle \mathbf {J} =nq\langle \mathbf {v} \rangle ,}$

${\displaystyle \mathbf {J} =\left({\frac {nq^{2}\tau }{m))\right)\mathbf {E} .}$

${\displaystyle \sigma (\omega )={\frac {\sigma _{0)){1+i\omega \tau )).}$

${\displaystyle E(t)=\Re (E_{0}e^{i\omega t});}$
${\displaystyle J(t)=\Re (\sigma (\omega )E_{0}e^{i\omega t}).}$

## 参考文献

1. ^ Drude, Paul. Zur Elektronentheorie der metalle. Annalen der Physik. 1900, 306 (3): 566.[永久失效链接]
2. ^ Drude, Paul. Zur Elektronentheorie der Metalle; II. Teil. Galvanomagnetische und thermomagnetische Effecte. Annalen der Physik. 1900, 308 (11): 369.[永久失效链接]
3. ^ Neil W. Ashcroft; N. David Mermin. Solid State Physics. Saunders College. 1976: 6–7. ISBN 0-03-083993-9.
4. ^ Edward M. Purcell. Electricity and Magnetism. McGraw-Hill. 1965: 117–122. ISBN 978-0070049086.
5. ^ David J. Griffiths. Introduction to Electrodynamics. Prentice-Hall. 1999: 289. ISBN 978-81-203-161-0 请检查|isbn=值 (帮助).
6. ^ Neil W. Ashcroft; N. David Mermin. Solid State Physics. Saunders College. 1976: 6–7. ISBN 0-03-083993-9.
7. ^ Neil W. Ashcroft; N. David Mermin. Solid State Physics. Saunders College. 1976: 11. ISBN 0-03-083993-9.
8. ^ Neil W. Ashcroft; N. David Mermin. Solid State Physics. Saunders College. 1976: 23. ISBN 0-03-083993-9.