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* Page found: Lösungen der Dirac-Gleichung (freies Teilchen) (eq math.2693.24)

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Weitere Eigenschaften der Dirac-Gleichung Eq: math.2685.39

Lösungen der Dirac-Gleichung (freies Teilchen) Eq: math.2693.24

Hash: 3435f6cbe4c73280992d41d82e709c97

TeX (original user input):

\begin{align}

& -{{{\tilde{\phi }}}_{-}}=-\left( E+m \right)\left( \begin{align}

& {{u}_{1}} \\

& {{u}_{2}} \\

& 0 \\

& 0 \\

\end{align} \right)-{{k}_{x}}\left( \begin{matrix}

0 & {{\sigma }_{x}}  \\

-{{\sigma }_{x}} & 0  \\

\end{matrix} \right)\left( \begin{align}

& {{u}_{1}} \\

& {{u}_{2}} \\

& 0 \\

& 0 \\

\end{align} \right)-{{k}_{y}}... \\

& =-\left( \begin{align}

& \underline{k}.\underline{\sigma }\left( \begin{align}

& {{u}_{1}} \\

& {{u}_{2}} \\

\end{align} \right) \\

& \left( E+m \right)\left( \begin{align}

& {{u}_{1}} \\

& {{u}_{2}} \\

\end{align} \right) \\

\end{align} \right)

\end{align}

TeX (checked):

{\begin{aligned}&-{{\tilde {\phi }}_{-}}=-\left(E+m\right)\left({\begin{aligned}&{{u}_{1}}\\&{{u}_{2}}\\&0\\&0\\\end{aligned}}\right)-{{k}_{x}}\left({\begin{matrix}0&{{\sigma }_{x}}\\-{{\sigma }_{x}}&0\\\end{matrix}}\right)\left({\begin{aligned}&{{u}_{1}}\\&{{u}_{2}}\\&0\\&0\\\end{aligned}}\right)-{{k}_{y}}...\\&=-\left({\begin{aligned}&{\underline {k}}.{\underline {\sigma }}\left({\begin{aligned}&{{u}_{1}}\\&{{u}_{2}}\\\end{aligned}}\right)\\&\left(E+m\right)\left({\begin{aligned}&{{u}_{1}}\\&{{u}_{2}}\\\end{aligned}}\right)\\\end{aligned}}\right)\end{aligned}}

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MathML (4.617 KB / 495 B) :

\begin{aligned} - {\tilde{ϕ}}_{-} = - (E + m) (\begin{aligned} u_{1} \\ u_{2} \\ 0 \\ 0 \end{aligned}) - k_{x} (\begin{matrix} 0 & σ_{x} \\ - σ_{x} & 0 \end{matrix}) (\begin{aligned} u_{1} \\ u_{2} \\ 0 \\ 0 \end{aligned}) - k_{y} . . . \\ = - (\begin{aligned} \underline{k} . \underline{σ} (\begin{aligned} u_{1} \\ u_{2} \end{aligned}) \\ (E + m) (\begin{aligned} u_{1} \\ u_{2} \end{aligned}) \end{aligned}) \end{aligned}

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Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

${\tilde{ϕ}}_{-}$

$E$

$m$

$u_{1}$

$u_{2}$

$k_{x}$

$σ_{x}$

$σ_{x}$

$u_{1}$

$u_{2}$

$k_{y}$

$\underline{k}$

$\underline{σ}$

$u_{1}$

$u_{2}$

$E$

$m$

$u_{1}$

$u_{2}$

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