Math Test

${\bf {B}}_{L}(0)=$ Failed to parse (syntax error): {\displaystyle \int \frac{Id{ {\bf{s}} }\times { {\bf{\hat}} {r}}}{{ {\bf{r}} }^2}} $\rightarrow -e{\bf {v}}\times {\left({\frac {-{\bf {r}}}{r^{3}}}\right)}=-2\mu _{B}{\frac {\bf {L}}{r^{3}}}$

Failed to parse (unknown function "\mathchar"): {\displaystyle {\mathchar'26\mkern-10mu\lambda} }

$N_{b}(t)=N_{b}(0)e^{-\gamma _{b}t}$

${\bf {\mu }}={\frac {q}{2m}}{\bf {L}}\equiv \gamma _{\ell }{\bf {L}}$

${\bf {L}}\equiv {\bf {r}}\times {\bf {p}}=m[{\bf {r}}\times {\bf {v}}]$

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*

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

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