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Display information for equation id:math.2665.45 on revision:2665
* Page found: Klein Gordon im (Vektor)Potential, Eichinvarianz (eq math.2665.45)
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Hash: 88a9f0ebf6566d11db26a878e179b92e
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\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}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>◻</mi><mo stretchy="false">=</mo><msubsup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msubsup><mo stretchy="false">−</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 stretchy="false" 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 stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></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 stretchy="false">−</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 stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mi>e</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi 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 class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>◻</mi><mo stretchy="false">+</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>Ψ</mi><mo stretchy="false">=</mo><mn>0</mn><mspace width="1em"></mspace><mo stretchy="false" 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 stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></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 stretchy="false">−</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 stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></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 stretchy="false">+</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">}</mo></mrow><mi>Ψ</mi><mo stretchy="false">=</mo><mn>0</mn><mspace width="1em"></mspace><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi alternate="1">ℏ</mi><mo stretchy="false">=</mo><mi>c</mi><mo stretchy="false">=</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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