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Display information for equation id:math.2657.7 on revision:2657

* Page found: Klein Gordon und Relativität (eq math.2657.7)

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Klein Gordon und Relativität Eq: math.2657.7

Hash: ad3a7f6bbf33769fa981510c1c2d732e

TeX (original user input):

\begin{align}

& \underline{{{{{x}'}}^{2}}-{{c}^{2}}{{{{t}'}}^{2}}}=\left( \begin{matrix}

{{x}'} & c{t}'  \\

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

1 & 0  \\

0 & -1  \\

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

& {{x}'} \\

& c{t}' \\

\end{align} \right)={{\gamma }^{2}}\left( \begin{matrix}

x & ct  \\

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

1 & -\beta   \\

-\beta  & 1  \\

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

1 & 0  \\

0 & -1  \\

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

1 & -\beta   \\

-\beta  & 1  \\

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

& x \\

& ct \\

\end{align} \right) \\

& ={{\gamma }^{2}}\left( \begin{matrix}

x & ct  \\

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

1-{{\beta }^{2}} & 0  \\

0 & -1+{{\beta }^{2}}  \\

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

& x \\

& ct \\

\end{align} \right)=\underline{{{x}^{2}}-{{c}^{2}}{{t}^{2}}}

\end{align}

TeX (checked):

{\begin{aligned}&{\underline {{{{x}'}^{2}}-{{c}^{2}}{{{t}'}^{2}}}}=\left({\begin{matrix}{{x}'}&c{t}'\\\end{matrix}}\right)\left({\begin{matrix}1&0\\0&-1\\\end{matrix}}\right)\left({\begin{aligned}&{{x}'}\\&c{t}'\\\end{aligned}}\right)={{\gamma }^{2}}\left({\begin{matrix}x&ct\\\end{matrix}}\right)\left({\begin{matrix}1&-\beta \\-\beta &1\\\end{matrix}}\right)\left({\begin{matrix}1&0\\0&-1\\\end{matrix}}\right)\left({\begin{matrix}1&-\beta \\-\beta &1\\\end{matrix}}\right)\left({\begin{aligned}&x\\&ct\\\end{aligned}}\right)\\&={{\gamma }^{2}}\left({\begin{matrix}x&ct\\\end{matrix}}\right)\left({\begin{matrix}1-{{\beta }^{2}}&0\\0&-1+{{\beta }^{2}}\\\end{matrix}}\right)\left({\begin{aligned}&x\\&ct\\\end{aligned}}\right)={\underline {{{x}^{2}}-{{c}^{2}}{{t}^{2}}}}\end{aligned}}

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\begin{aligned} \underline{{x^{'}}^{'}^{2} - c^{2} {t^{'}}^{'}^{2}} = (\begin{matrix} {x^{'}}^{'} & c {t^{'}}^{'} \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}) (\begin{aligned} {x^{'}}^{'} \\ c {t^{'}}^{'} \end{aligned}) = γ^{2} (\begin{matrix} x & c t \end{matrix}) (\begin{matrix} 1 & - β \\ - β & 1 \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}) (\begin{matrix} 1 & - β \\ - β & 1 \end{matrix}) (\begin{aligned} x \\ c t \end{aligned}) \\ = γ^{2} (\begin{matrix} x & c t \end{matrix}) (\begin{matrix} 1 - β^{2} & 0 \\ 0 & - 1 + β^{2} \end{matrix}) (\begin{aligned} x \\ c t \end{aligned}) = \underline{x^{2} - c^{2} t^{2}} \end{aligned}

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Identifiers

$x^{'}$

$c$

$t^{'}$

$x^{'}$

$c$

$t$

$x^{'}$

$c$

$t$

$γ$

$x$

$c$

$t$

$β$

$β$

$β$

$β$

$x$

$c$

$t$

$γ$

$x$

$c$

$t$

$β$

$β$

$x$

$c$

$t$

$x$

$c$

$t$

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