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Display information for equation id:math.2665.30 on revision:2665

* Page found: Klein Gordon im (Vektor)Potential, Eichinvarianz (eq math.2665.30)

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Klein Gordon im (Vektor)Potential, Eichinvarianz Eq: math.2665.30

Hash: 4cfceb80761c4b32663b06ad5499a033

TeX (original user input):

\begin{align}

& {{{\underline{D}}}_{\varphi }}\Psi \left( \underline{x},t \right){{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}=\left( \underline{\nabla }\Psi  \right){{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}+\Psi \mathfrak{i} \left( \underline{\nabla }\varphi  \right){{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}+{{{\underline{f}}}_{\varphi }}\left( \underline{x},t \right)\quad ={{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}\left( {{{\underline{D}}}_{\varphi }}+\mathfrak{i} \underline{\nabla }\varphi  \right)\Psi  \\

& D_{\varphi }^{0}\Psi \left( \underline{x},t \right){{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}=\quad \quad \quad \quad \quad \quad ={{e}^{\mathfrak{i} \varphi \left( \underline{x},t \right)}}\left( \underline{D}_{\varphi }^{0}+\mathfrak{i} {{\partial }_{t}}\varphi  \right)\Psi  \\

\end{align}

TeX (checked):

{\begin{aligned}&{{\underline {D}}_{\varphi }}\Psi \left({\underline {x}},t\right){{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}=\left({\underline {\nabla }}\Psi \right){{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}+\Psi {\mathfrak {i}}\left({\underline {\nabla }}\varphi \right){{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}+{{\underline {f}}_{\varphi }}\left({\underline {x}},t\right)\quad ={{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}\left({{\underline {D}}_{\varphi }}+{\mathfrak {i}}{\underline {\nabla }}\varphi \right)\Psi \\&D_{\varphi }^{0}\Psi \left({\underline {x}},t\right){{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}=\quad \quad \quad \quad \quad \quad ={{e}^{{\mathfrak {i}}\varphi \left({\underline {x}},t\right)}}\left({\underline {D}}_{\varphi }^{0}+{\mathfrak {i}}{{\partial }_{t}}\varphi \right)\Psi \\\end{aligned}}

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\begin{aligned} {\underline{D}}_{φ} Ψ (\underline{x}, t) e^{i φ (\underline{x}, t)} = (\underline{\nabla} Ψ) e^{i φ (\underline{x}, t)} + Ψ i (\underline{\nabla} φ) e^{i φ (\underline{x}, t)} + {\underline{f}}_{φ} (\underline{x}, t) = e^{i φ (\underline{x}, t)} ({\underline{D}}_{φ} + i \underline{\nabla} φ) Ψ \\ D_{φ}^{0} Ψ (\underline{x}, t) e^{i φ (\underline{x}, t)} = = e^{i φ (\underline{x}, t)} ({\underline{D}}_{φ}^{0} + i \partial_{t} φ) Ψ \end{aligned}

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Identifiers

${\underline{D}}_{φ}$

$Ψ$

$\underline{x}$

$t$

$e$

$i$

$φ$

$\underline{x}$

$t$

$Ψ$

$e$

$i$

$φ$

$\underline{x}$

$t$

$Ψ$

$i$

$φ$

$e$

$i$

$φ$

$\underline{x}$

$t$

${\underline{f}}_{φ}$

$\underline{x}$

$t$

$e$

$i$

$φ$

$\underline{x}$

$t$

${\underline{D}}_{φ}$

$i$

$φ$

$Ψ$

$D$

$φ$

$Ψ$

$\underline{x}$

$t$

$e$

$i$

$φ$

$\underline{x}$

$t$

$e$

$i$

$φ$

$\underline{x}$

$t$

$\underline{D}$

$φ$

$i$

$t$

$φ$

$Ψ$

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