# 三重态

## 两个自旋1/2的粒子

${\displaystyle \uparrow \uparrow ,\uparrow \downarrow ,\downarrow \uparrow ,\downarrow \downarrow }$

${\displaystyle |s_{1},m_{1}\rangle |s_{2},m_{2}\rangle =|s_{1},m_{1}\rangle \otimes |s_{2},m_{2}\rangle ,}$

${\displaystyle |s,m\rangle =\sum _{m_{1}+m_{2}=m}C_{m_{1}m_{2}m}^{s_{1}s_{2}s}|s_{1}m_{1}\rangle |s_{2}m_{2}\rangle }$

${\displaystyle |1/2,+1/2\rangle \;|1/2,+1/2\rangle \ (\uparrow \uparrow )}$
${\displaystyle |1/2,+1/2\rangle \;|1/2,-1/2\rangle \ (\uparrow \downarrow )}$
${\displaystyle |1/2,-1/2\rangle \;|1/2,+1/2\rangle \ (\downarrow \uparrow )}$
${\displaystyle |1/2,-1/2\rangle \;|1/2,-1/2\rangle \ (\downarrow \downarrow )}$

${\displaystyle \left.{\begin{array}{ll}|1,1\rangle &=\;\uparrow \uparrow \\|1,0\rangle &=\;(\uparrow \downarrow +\downarrow \uparrow )/{\sqrt {2}}\\|1,-1\rangle &=\;\downarrow \downarrow \end{array}}\right\}\quad s=1\quad \mathrm {(triplet)} }$

${\displaystyle \left.|0,0\rangle =(\uparrow \downarrow -\downarrow \uparrow )/{\sqrt {2}}\;\right\}\quad s=0\quad \mathrm {(singlet)} }$