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Display information for equation id:math.2615.11 on revision:2615

* Page found: Klein Gordon Gleichung (eq math.2615.11)

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Hash: a6fec2ca89db78f3d1726ee1652327ff

TeX (original user input):

\begin{align}

& \int{\rho \left( \underline{x},t \right){{d}^{d}}\underline{x}}={{\left( \frac{1}{2\pi } \right)}^{d}}\frac{1}{m}\int{\int{\int{{{\varphi }^{*}}\left( {\underline{k}} \right)\varphi \left( {{\underline{k}}'} \right){{e}^{i\left( \underline{k}-{\underline{k}}' \right)\underline{x}}}\omega \left( {{\underline{k}}'} \right){{d}^{d}}x}{{d}^{d}}k}{{d}^{d}}{k}'} \\

& =\frac{1}{m}\int{\omega \left( {\underline{k}} \right){{\left| \varphi \left( {\underline{k}} \right) \right|}^{2}}{{d}^{d}}\underline{k}}>0
\end{align}

TeX (checked):

{\begin{aligned}&\int {\rho \left({\underline {x}},t\right){{d}^{d}}{\underline {x}}}={{\left({\frac {1}{2\pi }}\right)}^{d}}{\frac {1}{m}}\int {\int {\int {{{\varphi }^{*}}\left({\underline {k}}\right)\varphi \left({{\underline {k}}'}\right){{e}^{i\left({\underline {k}}-{\underline {k}}'\right){\underline {x}}}}\omega \left({{\underline {k}}'}\right){{d}^{d}}x}{{d}^{d}}k}{{d}^{d}}{k}'}\\&={\frac {1}{m}}\int {\omega \left({\underline {k}}\right){{\left|\varphi \left({\underline {k}}\right)\right|}^{2}}{{d}^{d}}{\underline {k}}}>0\end{aligned}}

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\begin{aligned} \int ρ (\underline{x}, t) d^{d} \underline{x} = {(\frac{1}{2 π})}^{d} \frac{1}{m} \int \int \int φ^{*} (\underline{k}) φ ({\underline{k}}^{'}^{'}) e^{i (\underline{k} - {\underline{k}}^{'}^{'}) \underline{x}} ω ({\underline{k}}^{'}^{'}) d^{d} x d^{d} k d^{d} {k^{'}}^{'} \\ = \frac{1}{m} \int ω (\underline{k}) {| φ (\underline{k}) |}^{2} d^{d} \underline{k} > 0 \end{aligned}

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Identifiers

$ρ$

$\underline{x}$

$t$

$d$

$\underline{x}$

$π$

$d$

$m$

$φ$

$\underline{k}$

$φ$

${\underline{k}}^{'}$

$e$

$i$

$\underline{k}$

${\underline{k}}^{'}$

$\underline{x}$

$ω$

${\underline{k}}^{'}$

$x$

$d$

$k$

$d$

$d$

$k^{'}$

$m$

$ω$

$\underline{k}$

$φ$

$\underline{k}$

$d$

$\underline{k}$

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