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Display information for equation id:math.1777.42 on revision:1777

* Page found: Lippmann- Schwinger- Gleichung (eq math.1777.42)

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Lippmann- Schwinger- Gleichung Eq: math.1777.42

Hash: 357969d098c4f39ec311ffde45ff14ea

TeX (original user input):

\begin{align}

& {{G}_{+}}(\bar{R})=\frac{1}{{{\left( 2\pi  \right)}^{3}}}\int_{0}^{\infty }{dq}\int_{-1}^{1}{d\cos \vartheta }\int_{0}^{2\pi }{d\phi }\frac{{{q}^{2}}}{{{{\bar{k}}}^{2}}-{{{\bar{q}}}^{2}}+i\eta }{{e}^{iqR\cos \vartheta }} \\

& {{G}_{+}}(\bar{R})=\frac{1}{4{{\pi }^{2}}iqR}\int_{0}^{\infty }{dq}{{q}^{2}}\frac{{{e}^{iqR}}-{{e}^{-iqR}}}{q\left( {{{\bar{k}}}^{2}}-{{{\bar{q}}}^{2}}+i\eta  \right)} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{G}_{+}}({\bar {R}})={\frac {1}{{\left(2\pi \right)}^{3}}}\int _{0}^{\infty }{dq}\int _{-1}^{1}{d\cos \vartheta }\int _{0}^{2\pi }{d\phi }{\frac {{q}^{2}}{{{\bar {k}}^{2}}-{{\bar {q}}^{2}}+i\eta }}{{e}^{iqR\cos \vartheta }}\\&{{G}_{+}}({\bar {R}})={\frac {1}{4{{\pi }^{2}}iqR}}\int _{0}^{\infty }{dq}{{q}^{2}}{\frac {{{e}^{iqR}}-{{e}^{-iqR}}}{q\left({{\bar {k}}^{2}}-{{\bar {q}}^{2}}+i\eta \right)}}\\\end{aligned}}

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\begin{aligned} G_{+} (\bar{R}) = \frac{1}{{(2 π)}^{3}} \int_{0}^{\infty} d q \int_{- 1}^{1} d \cos ϑ \int_{0}^{2 π} d ϕ \frac{q^{2}}{{\bar{k}}^{2} - {\bar{q}}^{2} + i η} e^{i q R \cos ϑ} \\ G_{+} (\bar{R}) = \frac{1}{4 π^{2} i q R} \int_{0}^{\infty} d q q^{2} \frac{e^{i q R} - e^{- i q R}}{q ({\bar{k}}^{2} - {\bar{q}}^{2} + i η)} \end{aligned}

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Identifiers

$G_{+}$

$\bar{R}$

$π$

$q$

$ϑ$

$π$

$ϕ$

$q$

$\bar{k}$

$\bar{q}$

$i$

$η$

$e$

$i$

$q$

$R$

$ϑ$

$G_{+}$

$\bar{R}$

$π$

$i$

$q$

$R$

$q$

$q$

$e$

$i$

$q$

$R$

$e$

$i$

$q$

$R$

$q$

$\bar{k}$

$\bar{q}$

$i$

$η$

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