# 原子单位制

（重定向自原子单位

## 部分导出单位

${\displaystyle \!E_{\mathrm {h} }/a_{0}}$ 8.238 7225(14)×10-8 N 1044 N

## 简化后的量子力学与量子电动力学方程

${\displaystyle -{\frac {\hbar ^{2}}{2m_{e}}}\nabla ^{2}\psi (\mathbf {r} ,t)+V(\mathbf {r} )\psi (\mathbf {r} ,t)=i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {r} ,t)}$.

${\displaystyle -{\frac {1}{2}}\nabla ^{2}\psi (\mathbf {r} ,t)+V(\mathbf {r} )\psi (\mathbf {r} ,t)=i{\frac {\partial \psi }{\partial t}}(\mathbf {r} ,t)}$.

SI单位制下，氢原子薛定谔方程的哈密顿算符为：

${\displaystyle {\hat {H}}=-{{{\hbar ^{2}} \over {2m_{e}}}\nabla ^{2}}-{1 \over {4\pi \epsilon _{0}}}{{e^{2}} \over {r}}}$,

${\displaystyle {\hat {H}}=-{{{1} \over {2}}\nabla ^{2}}-{{1} \over {r}}}$.

${\displaystyle \nabla \cdot \mathbf {E} =4\pi \rho }$
${\displaystyle \nabla \cdot \mathbf {B} =0}$
${\displaystyle \nabla \times \mathbf {E} =-\alpha {\frac {\partial \mathbf {B} }{\partial t}}}$
${\displaystyle \nabla \times \mathbf {B} =\alpha \left({\frac {\partial \mathbf {E} }{\partial t}}+4\pi \mathbf {J} \right)}$

（磁场的原子单位的定义有多种方法。上面的麦克斯韦方程组采用了“高斯规范”，这使得平面波的电场与磁场在原子单位制下有着相同的数值，而在“洛仑兹力规范“下，因子α被吸收到磁感应强度B中。）

## 参考文献

• H. Shull and G. G. Hall, Atomic Units, Nature, volume 184, no. 4698, page 1559 (Nov. 14, 1959)
• G. Drake (ed.), Springer Handbook of Atomic, Molecular, and Optical Physics. Springer, 2nd ed., 2006