Nakajima-Zwanzig-Gleichung: Difference between revisions

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<math>\begin{align}
<math>\begin{align}
   & {{d}_{t}}\chi =L\chi  \\  
   & {{d}_{t}}\chi =L\chi  \\  
  & \chi =\mathcal{P}\chi +\mathcal{Q}\chi \\  
  & \chi =\mathcal{P}\chi +\mathcal{Q}\chi
\end{align}
<\math><math>
\begin{align}
  & {{d}_{t}}\left( \begin{matrix}
  & {{d}_{t}}\left( \begin{matrix}
   \mathcal{P}  \\
   \mathcal{P}  \\

Revision as of 18:12, 8 December 2010

Nakajima Zwanzig Equation Failed to parse (unknown function "\math"): {\displaystyle \begin{align} & {{d}_{t}}\chi =L\chi \\ & \chi =\mathcal{P}\chi +\mathcal{Q}\chi \end{align} <\math><math> \begin{align} & {{d}_{t}}\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)\chi =\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)L\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)\chi +\left( \begin{matrix} \mathcal{P} \\ \mathcal{Q} \\ \end{matrix} \right)L\left( \begin{matrix} \mathcal{Q} \\ \mathcal{P} \\ \end{matrix} \right)\chi \\ & \Rightarrow \mathcal{Q}\chi ={{e}^{\mathcal{Q}Lt}}Q{{\chi }_{0}}+\int '{{e}^{\mathcal{Q}Lt}}\mathcal{Q}L\mathcal{P}\chi (t-{t}') \\ & \Rightarrow {{\text{d}}_{t}}\mathcal{P}\chi =\mathcal{P}L\mathcal{P}\chi +\underbrace{\mathcal{P}{{e}^{\mathcal{Q}Lt}}Q{{\chi }_{0}}}_{=0}+\mathcal{P}L\int '{{e}^{\mathcal{Q}Lt}}\mathcal{Q}L\mathcal{P}\chi (t-{t}') \\ \end{align} }

Kategorie:Quantenmechanik