# 動量

## 古典力學中的動量

${\displaystyle \mathbf {p} =m\mathbf {v} }$

${\displaystyle {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t))={\frac {\mathrm {d} (m\mathbf {v} )}{\mathrm {d} t))=m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t))+v{\frac {\mathrm {d} m}{\mathrm {d} t))}$

${\displaystyle {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t))=m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t))}$

### 定理

${\displaystyle \sum \mathbf {I} =\Delta \mathbf {p} }$

## 碰撞中的動量守恆

${\displaystyle m_{1}\mathbf {v} _{1{\text{i))}+m_{2}\mathbf {v} _{2{\text{i))}=m_{1}\mathbf {v} _{1{\text{f))}+m_{2}\mathbf {v} _{2{\text{f))))$

## 彈性碰撞

${\displaystyle {\frac {1}{2))m_{1}v_{1{\text{i))}^{2}+{\frac {1}{2))m_{2}v_{2{\text{i))}^{2}={\frac {1}{2))m_{1}v_{1{\text{f))}^{2}+{\frac {1}{2))m_{2}v_{2{\text{f))}^{2))$

### 正向碰撞（一維）

${\displaystyle m_{1}v_{1{\text{i))}+m_{2}v_{2{\text{i))}=m_{1}v_{1{\text{f))}+m_{2}v_{2{\text{f))))$
${\displaystyle {\frac {1}{2))m_{1}v_{1{\text{i))}^{2}+{\frac {1}{2))m_{2}v_{2{\text{i))}^{2}={\frac {1}{2))m_{1}v_{1{\text{f))}^{2}+{\frac {1}{2))m_{2}v_{2{\text{f))}^{2))$

${\displaystyle v_{1{\text{f))}={\frac {m_{1}-m_{2)){m_{1}+m_{2))}v_{1{\text{i))}+{\frac {2m_{2)){m_{1}+m_{2))}v_{2{\text{i))))$
${\displaystyle v_{2{\text{f))}={\frac {2m_{1)){m_{1}+m_{2))}v_{1{\text{i))}+{\frac {m_{2}-m_{1)){m_{1}+m_{2))}v_{2{\text{i))))$

## 動量的現代定義

### 相對論力學中的動量

${\displaystyle \mathbf {p} =\gamma m\mathbf {u} }$

• ${\displaystyle m}$表示運動物體的靜止質量；
• ${\displaystyle \gamma ={\frac {1}{\sqrt {1-u^{2}/c^{2))))}$
• u表示物體與觀察者之間的相對速度；
• c表示光速

${\displaystyle \left({E \over c},p_{x},p_{y},p_{z}\right)}$

${\displaystyle E=\gamma mc^{2}\;}$

${\displaystyle \mathbf {p} \cdot \mathbf {p} -E^{2}/c^{2))$

#### 無靜止質量物體的動量

${\displaystyle p={\frac {h}{\lambda ))={\frac {E}{c))}$

${\displaystyle h}$表示普朗克常數
${\displaystyle \lambda }$表示光子的波長；
${\displaystyle E}$表示光子的能量
${\displaystyle c}$表示光速

### 量子力學中的動量

${\displaystyle \mathbf {p} ={\hbar \over i}\nabla =-i\hbar \nabla }$

## 參考文獻

1. ^ Daniel Garber. Descartes' Physics. (編) John Cottingham. The Cambridge Companion to Descartes. Cambridge: Cambridge University Press. 1992: 310–319. ISBN 0-521-36696-8.
2. ^ Rothman, Milton A. Discovering the natural laws : the experimental basis of physics 2nd. New York: Dover Publications. 1989: 83–88. ISBN 9780486261782.
3. ^ 人民教育出版社物理室《全日制普通高級中學教科書物理》第二冊ISBN 978-7-107-16500-9