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Display information for equation id:math.2232.12 on revision:2232
* Page found: Quantentheoretischer Zugang (eq math.2232.12)
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Hash: 54aa4824c72bd813e5ef2fd347e547d4
TeX (original user input):
{{\sum }_{\vec{k}\in \text{3-Dim Raum}}}=\sum\limits_{\text{k}}{\frac{{{\Delta }^{\text{3}}}k}{\underbrace{{{\Delta }^{\text{3}}}k}_{\Delta {{k}_{x\Delta }}\Delta {{k}_{y}}\Delta {{k}_{z}}}}}={{\left( \frac{L}{2\pi } \right)}^{3}}\sum\limits_{\text{k}}{{{\Delta }^{\text{3}}}k}\to {{\left( \frac{L}{2\pi } \right)}^{3}}\int{{{d}^{\text{3}}}k}
TeX (checked):
{{\sum }_{{\vec {k}}\in {\text{3-Dim Raum}}}}=\sum \limits _{\text{k}}{\frac {{{\Delta }^{\text{3}}}k}{\underbrace {{{\Delta }^{\text{3}}}k} _{\Delta {{k}_{x\Delta }}\Delta {{k}_{y}}\Delta {{k}_{z}}}}}={{\left({\frac {L}{2\pi }}\right)}^{3}}\sum \limits _{\text{k}}{{{\Delta }^{\text{3}}}k}\to {{\left({\frac {L}{2\pi }}\right)}^{3}}\int {{{d}^{\text{3}}}k}
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MathML (2.945 KB / 491 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mo texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>→</mo></mover></mrow></mrow><mo>∈</mo><mrow data-mjx-texclass="ORD"><mtext>3-Dim Raum</mtext></mrow></mrow></mrow></msub></mstyle><mo>=</mo><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>k</mtext></mrow></mrow></munder><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>3</mtext></mrow></mrow></msup><mi>k</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><msup><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>3</mtext></mrow></mrow></msup><mi>k</mi></mrow><mo>⏟</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">Δ</mi><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>x</mi><mi mathvariant="normal">Δ</mi></mrow></mrow></msub><mi mathvariant="normal">Δ</mi><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>y</mi></mrow></msub><mi mathvariant="normal">Δ</mi><msub><mi>k</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub></mrow></mrow></munder></mrow></mfrac></mrow><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>L</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><munder><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>k</mtext></mrow></mrow></munder><mrow data-mjx-texclass="ORD"><msup><mi mathvariant="normal">Δ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>3</mtext></mrow></mrow></msup><mi>k</mi></mrow><mo accent="false">→</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>L</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>3</mtext></mrow></mrow></msup><mi>k</mi></mrow></mrow></math>
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