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Display information for equation id:math.2693.20 on revision:2693

* Page found: Lösungen der Dirac-Gleichung (freies Teilchen) (eq math.2693.20)

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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 (2.533 KB / 467 B) :

(γμkμm)(γνkν+m)=γμkμγνkνm2=E2k2m2=0,mit(γμ)2=±1,E2=k2+m2,=c=1
<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"><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 stretchy="false"></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 stretchy="false">+</mo><mi>m</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</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 stretchy="false"></mo><msup><mi>m</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false"></mo><msup><mi>k</mi><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 stretchy="false">=</mo><mn>0</mn><mo>,</mo><mspace width="1em"></mspace></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><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 stretchy="false">=</mo><mo stretchy="false">±</mo><mn>1</mn><mo>,</mo><msup><mi>E</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>k</mi><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>,</mo><mi alternate="1"></mi><mo stretchy="false">=</mo><mi>c</mi><mo stretchy="false">=</mo><mn>1</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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  • γ
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  • ν
  • kν
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  • γ
  • μ
  • kμ
  • γ
  • ν
  • kν
  • m
  • E
  • k
  • m
  • m
  • i
  • t
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  • E
  • k
  • m
  • c

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