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Display information for equation id:math.1325.190 on revision:1325

* Page found: Der Hamiltonsche kanonische Formalismus (eq math.1325.190)

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Occurrences on the following pages:

Hash: 1a3fc5611cb7507544b1ea033d225fd5

TeX (original user input):

\begin{align}
  & {{A}^{2}}=\left( \begin{matrix}
   0 & 1  \\
   -{{\omega }_{0}}^{2} & 0  \\
\end{matrix} \right)\left( \begin{matrix}
   0 & 1  \\
   -{{\omega }_{0}}^{2} & 0  \\
\end{matrix} \right)=-{{\omega }_{0}}^{2}1 \\ 
 & {{A}^{2n}}={{(-1)}^{2n}}{{\omega }_{0}}^{2n}1 \\ 
 & {{A}^{2n+1}}={{(-1)}^{n}}{{\omega }_{0}}^{2n+1}\frac{1}{{{\omega }_{0}}}A \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{{A}^{2}}=\left({\begin{matrix}0&1\\-{{\omega }_{0}}^{2}&0\\\end{matrix}}\right)\left({\begin{matrix}0&1\\-{{\omega }_{0}}^{2}&0\\\end{matrix}}\right)=-{{\omega }_{0}}^{2}1\\&{{A}^{2n}}={{(-1)}^{2n}}{{\omega }_{0}}^{2n}1\\&{{A}^{2n+1}}={{(-1)}^{n}}{{\omega }_{0}}^{2n+1}{\frac {1}{{\omega }_{0}}}A\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

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MathML (experimentell; keine Bilder) rendering

MathML (2.95 KB / 460 B) :

A2=(01ω020)(01ω020)=ω021A2n=(1)2nω02n1A2n+1=(1)nω02n+11ω0A
<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><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>&#x2212;</mo><msup><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mo>&#x2212;</mo><msup><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>&#x2212;</mo><msup><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi></mrow></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi></mrow></mrow></msup><msup><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi></mrow></mrow></msup><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mo>&#x2212;</mo><mn>1</mn><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msup><msup><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msub><mi>&#x03C9;</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mfrac></mrow><mi>A</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Der Hamiltonsche kanonische Formalismus page

Identifiers

  • A
  • ω0
  • ω0
  • ω0
  • A
  • n
  • n
  • ω0
  • n
  • A
  • n
  • n
  • ω0
  • n
  • ω0
  • A

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