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Feb 09, 20251 min read

$↑ = \frac{1}{2}, \frac{1}{2} ⟩$

Represents $∣ s, m_{s} ⟩$ , or a state with a spin $s$ and spin quantum number $m_{s}$

$\displaystyle \uparrow \,=\left\lvert \frac{1}{2}, \frac{1}{2}\right\rangle$
$\displaystyle \downarrow \,=\left\lvert \frac{1}{2}, -\frac{1}{2}\right\rangle$