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Display information for equation id:math.1772.62 on revision:1772
* Page found: Lippmann- Schwinger- Gleichung (eq math.1772.62)
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Hash: 5ca45af3bd3e2c79489aa1647f8c6dc4
TeX (original user input):
\begin{align}
& \left| {{\Psi }^{(+)}} \right\rangle =\left| \Phi \right\rangle +\frac{1}{\left( E-{{{\hat{H}}}_{0}}+i\varepsilon \right)}{{{\hat{H}}}^{(1)}}\left| {{\Psi }^{(+)}} \right\rangle \\
& \frac{1}{\left( E-{{{\hat{H}}}_{0}} \right)}:={{\left( E-{{{\hat{H}}}_{0}} \right)}^{-1}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\left|{{\Psi }^{(+)}}\right\rangle =\left|\Phi \right\rangle +{\frac {1}{\left(E-{{\hat {H}}_{0}}+i\varepsilon \right)}}{{\hat {H}}^{(1)}}\left|{{\Psi }^{(+)}}\right\rangle \\&{\frac {1}{\left(E-{{\hat {H}}_{0}}\right)}}:={{\left(E-{{\hat {H}}_{0}}\right)}^{-1}}\\\end{aligned}}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msup><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">Φ</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>+</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="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><mi>i</mi><mi>ε</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msup><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo>+</mo><mo stretchy="false">)</mo></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">⟩</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mfrac></mrow><mi>:</mi><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mn>1</mn></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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