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Display information for equation id:math.1515.62 on revision:1515

* Page found: Normalschwingungen (eq math.1515.62)

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\begin{align}
  & \sum\limits_{k,l}{{{A}_{l}}^{a}{{T}_{lk}}{{A}_{k}}^{a}=m\sum\limits_{k}{{{\left| {{A}_{k}}^{a} \right|}^{2}}}=1} \\
 & \Rightarrow \left( \begin{matrix}
   {{A}_{1}}^{1}  \\
   {{A}_{2}}^{1}  \\
\end{matrix} \right)=\frac{1}{\sqrt{2m}}\left( \begin{matrix}
   1  \\
   1  \\
\end{matrix} \right) \\
 & \left( \begin{matrix}
   {{A}_{1}}^{2}  \\
   {{A}_{2}}^{2}  \\
\end{matrix} \right)=\frac{1}{\sqrt{2m}}\left( \begin{matrix}
   1  \\
   -1  \\
\end{matrix} \right) \\
\end{align}

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MathML (32.077 KB / 3.474 KB) :

∑ k , l A l a ⁢ T l ⁢ k ⁢ A k a = m ⁢ ∑ k | A k a | 2 = 1 ⇒ ( A 1 1 A 2 1 ) = 1 2 ⁢ m ⁢ ( 1 1 ) ( A 1 2 A 2 2 ) = 1 2 ⁢ m ⁢ ( 1 - 1 ) missing-subexpression subscript 𝑘 𝑙 superscript subscript 𝐴 𝑙 𝑎 subscript 𝑇 𝑙 𝑘 superscript subscript 𝐴 𝑘 𝑎 𝑚 subscript 𝑘 superscript superscript subscript 𝐴 𝑘 𝑎 2 1 missing-subexpression ⇒ absent superscript subscript 𝐴 1 1 superscript subscript 𝐴 2 1 1 2 𝑚 1 1 missing-subexpression superscript subscript 𝐴 1 2 superscript subscript 𝐴 2 2 1 2 𝑚 1 1 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\sum\limits_{k,l}{{{% A}_{l}}^{a}{{T}_{lk}}{{A}_{k}}^{a}=m\sum\limits_{k}{{{\left|{{A}_{k}}^{a}% \right|}^{2}}}=1}\\ &\displaystyle\Rightarrow\left(\begin{matrix}{{A}_{1}}^{1}\\ {{A}_{2}}^{1}\\ \end{matrix}\right)=\frac{1}{\sqrt{2m}}\left(\begin{matrix}1\\ 1\\ \end{matrix}\right)\\ &\displaystyle\left(\begin{matrix}{{A}_{1}}^{2}\\ {{A}_{2}}^{2}\\ \end{matrix}\right)=\frac{1}{\sqrt{2m}}\left(\begin{matrix}1\\ -1\\ \end{matrix}\right)\\ \end{aligned}}}

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∑k,lAlaTlkAka=m∑k|Aka|2=1⇒(A11A21)=12m(11)(A12A22)=12m(1−1)

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