Math Test

This is a test ${\frac {\alpha }{\sqrt {\gamma +1}}}$

units: Failed to parse (unknown function "\unit"): {\displaystyle \frac{1}{\unit{1}{\kelvin}} } Failed to parse (unknown function "\unit"): {\displaystyle \unit{10}{\reciprocal\metre}}

mathbold: Failed to parse (unknown function "\bm"): {\displaystyle \bm{V}}

bold ${\bf {foo}}$ ${\textbf {foo}}$

italic ${\it {test}}$

cal ${\cal {C}}$

left right $\left[{\frac {x}{y}}\right]$ $\left|\Psi \right\rangle$

align*

${\begin{aligned}{\frac {d}{dt}}{\hat {\mu }}_{x}&=-{\frac {i\gamma ^{2}}{\hbar }}B_{0}i\hbar {\hat {L}}_{y}=\gamma ^{2}{\hat {L}}_{y}B_{0}={\hat {\mu }}_{y}\gamma B_{0}\\{\frac {d}{dt}}{\hat {\mu }}_{y}&=-\mu _{x}\gamma B_{0}\\{\frac {d}{dt}}{\hat {\mu }}_{z}&=0\end{aligned}}$

${\begin{aligned}\left\langle {\hat {O}}\right\rangle &=Tr\left({\hat {O}}{\hat {\rho }}\right)=\Sigma _{n}\left\langle n\right|{\hat {O}}{\hat {\rho }}\left|n\right\rangle \end{aligned}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} =\Sigma_{n^\prime n} \left\langle n\right| \hat O \left|n^\prime\right\rangle \left\langle n^\prime\right| \hat \rho \left|n\right\rangle \\ \left\langle \hat O\right\rangle} &= \Sigma_{nn^\prime}O_{nn^\prime}\rho_{n^\prime n O_{nn^\prime}= \left\langle n\right| \hat O \left|n^\prime\right\rangle \end{align}}