Math Test

much less than? $x\ll y$

Failed to parse (syntax error): {\displaystyle t \ll \frac{1}{\Gamma}, \frac{1}{\Gamma'}, \frac{1}{\Gamma"}, \ldots}

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*

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

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