Math Test

Equations with numbers

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

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

(1.3)

Misc Math

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*

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

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