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Display information for equation id:math.2687.17 on revision:2687

* Page found: Lösungen der Dirac-Gleichung (freies Teilchen) (eq math.2687.17)

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Lösungen der Dirac-Gleichung (freies Teilchen) Eq: math.2693.17

Hash: a29ec76b0792e3c6782c7029658aa471

TeX (original user input):

\begin{align}

& \left( {{\gamma }^{0}}E-{{\gamma }^{1}}{{k}_{x}}-{{\gamma }^{2}}{{k}_{y}}-{{\gamma }^{3}}{{k}_{z}}-m \right){{\phi }_{+}}=0\Leftrightarrow \left( {{\gamma }^{\mu }}{{k}_{\mu }}-m \right){{\phi }_{+}}=0 \\

& \left( -{{\gamma }^{0}}E+{{\gamma }^{1}}{{k}_{x}}+{{\gamma }^{2}}{{k}_{y}}+{{\gamma }^{3}}{{k}_{z}}-m \right){{\phi }_{-}}=0\Leftrightarrow \left( {{\gamma }^{\mu }}{{k}_{\mu }}+m \right){{\phi }_{-}}=0 \\

\end{align}

TeX (checked):

{\begin{aligned}&\left({{\gamma }^{0}}E-{{\gamma }^{1}}{{k}_{x}}-{{\gamma }^{2}}{{k}_{y}}-{{\gamma }^{3}}{{k}_{z}}-m\right){{\phi }_{+}}=0\Leftrightarrow \left({{\gamma }^{\mu }}{{k}_{\mu }}-m\right){{\phi }_{+}}=0\\&\left(-{{\gamma }^{0}}E+{{\gamma }^{1}}{{k}_{x}}+{{\gamma }^{2}}{{k}_{y}}+{{\gamma }^{3}}{{k}_{z}}-m\right){{\phi }_{-}}=0\Leftrightarrow \left({{\gamma }^{\mu }}{{k}_{\mu }}+m\right){{\phi }_{-}}=0\\\end{aligned}}

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MathML (3.135 KB / 424 B) :

\begin{matrix} (γ^{0} E - γ^{1} k_{x} - γ^{2} k_{y} - γ^{3} k_{z} - m) ϕ_{+} = 0 \Leftrightarrow (γ^{μ} k_{μ} - m) ϕ_{+} = 0 \\ (- γ^{0} E + γ^{1} k_{x} + γ^{2} k_{y} + γ^{3} k_{z} - m) ϕ_{-} = 0 \Leftrightarrow (γ^{μ} k_{μ} + m) ϕ_{-} = 0 \end{matrix}

<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"><mn>0</mn></mrow></msup><mi>E</mi><mo stretchy="false">−</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">−</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mo stretchy="false">−</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><mo stretchy="false">−</mo><mi>m</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mo stretchy="false">=</mo><mn>0</mn><mo stretchy="false">⇔</mo><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><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></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><mo stretchy="false">−</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msup><mi>E</mi><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>x</mi></mrow></msub><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mo stretchy="false">+</mo><msup><mi>γ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><mo stretchy="false">−</mo><mi>m</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">−</mo></mrow></msub><mo stretchy="false">=</mo><mn>0</mn><mo stretchy="false">⇔</mo><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><msub><mi>ϕ</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">−</mo></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

$γ$

$E$

$γ$

$k_{x}$

$γ$

$k_{y}$

$γ$

$k_{z}$

$m$

$ϕ_{+}$

$γ$

$μ$

$k_{μ}$

$m$

$ϕ_{+}$

$γ$

$E$

$γ$

$k_{x}$

$γ$

$k_{y}$

$γ$

$k_{z}$

$m$

$ϕ_{-}$

$γ$

$μ$

$k_{μ}$

$m$

$ϕ_{-}$

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