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Display information for equation id:math.2687.20 on revision:2687
* Page found: Lösungen der Dirac-Gleichung (freies Teilchen) (eq math.2687.20)
(force rerendering)Occurrences on the following pages:
Hash: aa1df5960672b0a28f99b74b86729d73
TeX (original user input):
\begin{align}
& \left( {{\gamma }^{\mu }}{{k}_{\mu }}-m \right)\left( {{\gamma }^{\nu }}{{k}_{\nu }}+m \right)={{\gamma }^{\mu }}{{k}_{\mu }}{{\gamma }^{\nu }}{{k}_{\nu }}-{{m}^{2}}={{E}^{2}}-{{k}^{2}}-{{m}^{2}}=0,\quad \\
& mit\,{{\left( {{\gamma }^{\mu }} \right)}^{2}}=\pm 1,{{E}^{2}}={{k}^{2}}+{{m}^{2}},\hbar =c=1 \\
\end{align}
TeX (checked):
{\begin{aligned}&\left({{\gamma }^{\mu }}{{k}_{\mu }}-m\right)\left({{\gamma }^{\nu }}{{k}_{\nu }}+m\right)={{\gamma }^{\mu }}{{k}_{\mu }}{{\gamma }^{\nu }}{{k}_{\nu }}-{{m}^{2}}={{E}^{2}}-{{k}^{2}}-{{m}^{2}}=0,\quad \\&mit\,{{\left({{\gamma }^{\mu }}\right)}^{2}}=\pm 1,{{E}^{2}}={{k}^{2}}+{{m}^{2}},\hbar =c=1\\\end{aligned}}
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MathML (2.437 KB / 478 B) :
<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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><mo>−</mo><mi>m</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo>+</mo><mi>m</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msub><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>ν</mi></mrow></msub><mo>−</mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mi>k</mi><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>=</mo><mn>0</mn><mo>,</mo><mspace width="1em"></mspace></mtd></mtr><mtr><mtd></mtd><mtd><mi>m</mi><mi>i</mi><mi>t</mi><mspace width="0.167em"></mspace><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mo>±</mo><mn>1</mn><mo>,</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mi>k</mi><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>,</mo><mi data-mjx-alternate="1">ℏ</mi><mo>=</mo><mi>c</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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