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Display information for equation id:math.1769.28 on revision:1769

* Page found: Lippmann- Schwinger- Gleichung (eq math.1769.28)

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TeX (original user input):

\begin{align}

& {{G}_{+}}(\bar{r},\bar{r}\acute{\ })=\frac{1}{{{\left( 2\pi  \right)}^{3}}}\int_{{}}^{{}}{{{d}^{3}}q}{{{\tilde{G}}}_{+}}(\bar{q}){{e}^{i\bar{q}\left( \bar{r}-\bar{r}\acute{\ } \right)}} \\

& {{{\tilde{G}}}_{+}}(\bar{q})=\frac{1}{{{{\bar{k}}}^{2}}-{{{\bar{q}}}^{2}}+i\eta } \\

\end{align}

TeX (checked):

{\begin{aligned}&{{G}_{+}}({\bar {r}},{\bar {r}}{\acute {\ }})={\frac {1}{{\left(2\pi \right)}^{3}}}\int _{}^{}{{{d}^{3}}q}{{\tilde {G}}_{+}}({\bar {q}}){{e}^{i{\bar {q}}\left({\bar {r}}-{\bar {r}}{\acute {\ }}\right)}}\\&{{\tilde {G}}_{+}}({\bar {q}})={\frac {1}{{{\bar {k}}^{2}}-{{\bar {q}}^{2}}+i\eta }}\\\end{aligned}}

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MathML (2.672 KB / 543 B) :

G+(r¯,r¯ ´)=1(2π)3d3qG~+(q¯)eiq¯(r¯r¯ ´)G~+(q¯)=1k¯2q¯2+iη
<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"><msub><mi>G</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo>,</mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>π</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><msubsup><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>q</mi></mrow><msub><mover><mi>G</mi><mo>~</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mover><mi>q</mi><mo>¯</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false"></mo><mover><mi>r</mi><mo>¯</mo></mover><mover><mtext>&#160;</mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mover><mi>G</mi><mo>~</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><mo stretchy="false">(</mo><mover><mi>q</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mover><mi>k</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false"></mo><msup><mover><mi>q</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi>i</mi><mi>η</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Identifiers

  • G+
  • r¯
  • r¯
  •  ´
  • π
  • q
  • G~+
  • q¯
  • e
  • i
  • q¯
  • r¯
  • r¯
  •  ´
  • G~+
  • q¯
  • k¯
  • q¯
  • i
  • η

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