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* Page found: Das Wasserstoffatom (relativistsich) (eq math.1826.9)

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Das Wasserstoffatom (relativistsich) Eq: math.1826.9

Hash: 7bedf312b30190f7d8b57e073182dcda

TeX (original user input):

\begin{align}

& {{\left( \hbar Q \right)}^{2}}={{L}^{2}}+\hbar \tilde{\bar{\sigma }}\bar{L}+{{\hbar }^{2}}={{\left( \bar{L}+\frac{\hbar }{2}\tilde{\bar{\sigma }} \right)}^{2}}+\frac{{{\hbar }^{2}}}{4} \\

& mit\ {{\left( \bar{L}+\frac{\hbar }{2}\tilde{\bar{\sigma }} \right)}^{2}}={{L}^{2}}+\hbar \tilde{\bar{\sigma }}\bar{L}+\frac{{{\hbar }^{2}}}{4}{{{\tilde{\bar{\sigma }}}}^{2}} \\

& {{{\tilde{\bar{\sigma }}}}^{2}}=3 \\

& \left( \bar{L}+\frac{\hbar }{2}\tilde{\bar{\sigma }} \right)=\bar{J} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{\left(\hbar Q\right)}^{2}}={{L}^{2}}+\hbar {\tilde {\bar {\sigma }}}{\bar {L}}+{{\hbar }^{2}}={{\left({\bar {L}}+{\frac {\hbar }{2}}{\tilde {\bar {\sigma }}}\right)}^{2}}+{\frac {{\hbar }^{2}}{4}}\\&mit\ {{\left({\bar {L}}+{\frac {\hbar }{2}}{\tilde {\bar {\sigma }}}\right)}^{2}}={{L}^{2}}+\hbar {\tilde {\bar {\sigma }}}{\bar {L}}+{\frac {{\hbar }^{2}}{4}}{{\tilde {\bar {\sigma }}}^{2}}\\&{{\tilde {\bar {\sigma }}}^{2}}=3\\&\left({\bar {L}}+{\frac {\hbar }{2}}{\tilde {\bar {\sigma }}}\right)={\bar {J}}\\\end{aligned}}

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MathML (4.913 KB / 506 B) :

\begin{aligned} {(ℏ Q)}^{2} = L^{2} + ℏ \tilde{\bar{σ}} \bar{L} + ℏ^{2} = {(\bar{L} + \frac{ℏ}{2} \tilde{\bar{σ}})}^{2} + \frac{ℏ^{2}}{4} \\ m i t {(\bar{L} + \frac{ℏ}{2} \tilde{\bar{σ}})}^{2} = L^{2} + ℏ \tilde{\bar{σ}} \bar{L} + \frac{ℏ^{2}}{4} {\tilde{\bar{σ}}}^{2} \\ {\tilde{\bar{σ}}}^{2} = 3 \\ (\bar{L} + \frac{ℏ}{2} \tilde{\bar{σ}}) = \bar{J} \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$Q$

$L$

$\tilde{\bar{σ}}$

$\bar{L}$

$\bar{L}$

$\tilde{\bar{σ}}$

$m$

$i$

$t$

$\bar{L}$

$\tilde{\bar{σ}}$

$L$

$\tilde{\bar{σ}}$

$\bar{L}$

$\tilde{\bar{σ}}$

$\tilde{\bar{σ}}$

$\bar{L}$

$\tilde{\bar{σ}}$

$\bar{J}$

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