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Display information for equation id:math.2663.45 on revision:2663
* Page found: Klein Gordon im (Vektor)Potential, Eichinvarianz (eq math.2663.45)
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Hash: 88a9f0ebf6566d11db26a878e179b92e
TeX (original user input):
\begin{align}
& \square =\partial _{t}^{2}-{{{\underline{\nabla }}}^{2}}\quad \to {{\left( {{\partial }_{t}}+\mathfrak{i} e\varphi \right)}^{2}}-{{\left( \underline{\nabla }-\frac{\mathfrak{i} e}{\hbar }\underline{A} \right)}^{2}} \\
& \left( \square +{{m}^{2}} \right)\Psi =0\quad \to \left\{ {{\left( {{\partial }_{t}}+\mathfrak{i} e\varphi \right)}^{2}}-{{\left( \underline{\nabla }-\mathfrak{i} e\underline{A} \right)}^{2}}+{{m}^{2}} \right\}\Psi =0\quad \left( \hbar =c=1 \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&\square =\partial _{t}^{2}-{{\underline {\nabla }}^{2}}\quad \to {{\left({{\partial }_{t}}+{\mathfrak {i}}e\varphi \right)}^{2}}-{{\left({\underline {\nabla }}-{\frac {{\mathfrak {i}}e}{\hbar }}{\underline {A}}\right)}^{2}}\\&\left(\square +{{m}^{2}}\right)\Psi =0\quad \to \left\{{{\left({{\partial }_{t}}+{\mathfrak {i}}e\varphi \right)}^{2}}-{{\left({\underline {\nabla }}-{\mathfrak {i}}e{\underline {A}}\right)}^{2}}+{{m}^{2}}\right\}\Psi =0\quad \left(\hbar =c=1\right)\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>◻</mi><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></munderover></mstyle><mo>−</mo><msup><mrow data-mjx-texclass="ORD"><munder><mi mathvariant="normal">∇</mi><mo>_</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mspace width="1em"></mspace><mo accent="false">→</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mi>e</mi><mi>φ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi mathvariant="normal">∇</mi><mo>_</mo></munder></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mi>e</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><munder><mi>A</mi><mo>_</mo></munder></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>◻</mi><mo>+</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi mathvariant="normal">Ψ</mi><mo>=</mo><mn>0</mn><mspace width="1em"></mspace><mo accent="false">→</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo>+</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mi>e</mi><mi>φ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><munder><mi mathvariant="normal">∇</mi><mo>_</mo></munder></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="fraktur">i</mi></mrow></mrow><mi>e</mi><mrow data-mjx-texclass="ORD"><munder><mi>A</mi><mo>_</mo></munder></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">}</mo></mrow><mi mathvariant="normal">Ψ</mi><mo>=</mo><mn>0</mn><mspace width="1em"></mspace><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi data-mjx-alternate="1">ℏ</mi><mo>=</mo><mi>c</mi><mo>=</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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