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Display information for equation id:math.1750.28 on revision:1750

* Page found: Zeitunabhängige Störungsrechnung bei Entartung (eq math.1750.28)

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Hash: 3029e28f6a40c191e6845a20712f86b5

TeX (original user input): 

\begin{align}

& \left| \begin{matrix}

{{{\hat{V}}}_{11}}-{{E}_{k}}^{(1)} & {{{\hat{V}}}_{12}}  \\

{{{\hat{V}}}_{21}} & {{{\hat{V}}}_{22}}-{{E}_{k}}^{(1)}  \\

\end{matrix} \right|=0 \\

& {{\left( {{E}_{k}}^{(1)} \right)}^{2}}-\left( {{{\hat{V}}}_{11}}+{{{\hat{V}}}_{22}} \right){{E}_{k}}^{(1)}+\left( {{{\hat{V}}}_{11}}{{{\hat{V}}}_{22}}-{{{\hat{V}}}_{12}}{{{\hat{V}}}_{21}} \right)=0 \\

& {{{\hat{V}}}_{12}}{{{\hat{V}}}_{21}}={{\left| {{{\hat{V}}}_{12}} \right|}^{2}} \\
& \Rightarrow {{E}_{k}}^{(1)}=\frac{1}{2}\left[ \left( {{{\hat{V}}}_{11}}+{{{\hat{V}}}_{22}} \right)\pm \sqrt{{{\left( {{{\hat{V}}}_{11}}-{{{\hat{V}}}_{22}} \right)}^{2}}+4{{\left| {{{\hat{V}}}_{12}} \right|}^{2}}} \right] \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left|{\begin{matrix}{{\hat {V}}_{11}}-{{E}_{k}}^{(1)}&{{\hat {V}}_{12}}\\{{\hat {V}}_{21}}&{{\hat {V}}_{22}}-{{E}_{k}}^{(1)}\\\end{matrix}}\right|=0\\&{{\left({{E}_{k}}^{(1)}\right)}^{2}}-\left({{\hat {V}}_{11}}+{{\hat {V}}_{22}}\right){{E}_{k}}^{(1)}+\left({{\hat {V}}_{11}}{{\hat {V}}_{22}}-{{\hat {V}}_{12}}{{\hat {V}}_{21}}\right)=0\\&{{\hat {V}}_{12}}{{\hat {V}}_{21}}={{\left|{{\hat {V}}_{12}}\right|}^{2}}\\&\Rightarrow {{E}_{k}}^{(1)}={\frac {1}{2}}\left[\left({{\hat {V}}_{11}}+{{\hat {V}}_{22}}\right)\pm {\sqrt {{{\left({{\hat {V}}_{11}}-{{\hat {V}}_{22}}\right)}^{2}}+4{{\left|{{\hat {V}}_{12}}\right|}^{2}}}}\right]\\\end{aligned}}

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MathML (7.248 KB / 613 B) :

|V^11−Ek(1)V^12V^21V^22−Ek(1)|=0(Ek(1))2−(V^11+V^22)Ek(1)+(V^11V^22−V^12V^21)=0V^12V^21=|V^12|2⇒Ek(1)=12[(V^11+V^22)±(V^11−V^22)2+4|V^12|2]
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Similar pages

Calculated based on the variables occurring on the entire Zeitunabhängige Störungsrechnung bei Entartung page

Identifiers

  • V^11
  • Ek
  • V^12
  • V^21
  • V^22
  • Ek
  • Ek
  • V^11
  • V^22
  • Ek
  • V^11
  • V^22
  • V^12
  • V^21
  • V^12
  • V^21
  • V^12
  • Ek
  • V^11
  • V^22
  • V^11
  • V^22
  • V^12

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“