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Display information for equation id:math.2232.70 on revision:2232

* Page found: Quantentheoretischer Zugang (eq math.2232.70)

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Quantentheoretischer Zugang Eq: math.2232.70

Hash: 737206c481da4b2450b538ab4cdce9b4

TeX (original user input):

\begin{align}
  & \left\langle {{O}_{S}} \right\rangle =\operatorname{Tr}\left( \rho {{O}_{s}} \right)=\underbrace{\sum\limits_{n}{\left\langle  n \right|\rho {{O}_{s}}\left| n \right\rangle }}_{\begin{smallmatrix}
 n\text{ vollst}\text{. System im} \\
 \text{Vielteilchenraum des }
 \\
 \text{Systems}
\end{smallmatrix}} \\
 & =\sum\limits_{n}{\left\langle  n \right|\underbrace{\sum\limits_{i}{{{w}_{i}}\left| {{\Psi }_{i}} \right\rangle \left\langle  {{\Psi }_{i}} \right|}}_{\rho }{{O}_{s}}\left| n \right\rangle }=\sum\limits_{i}{{{w}_{i}}\left\langle  {{\Psi }_{i}} \right|\underbrace{\sum\limits_{n}{\left| n \right\rangle \left\langle  n \right|}}_{1}}{{O}_{s}}\left| {{\Psi }_{i}} \right\rangle  \\
 & =\sum\limits_{i}{{{w}_{i}}\underbrace{\left\langle  {{\Psi }_{i}} \right|{{O}_{s}}\left| {{\Psi }_{i}} \right\rangle }_{\begin{smallmatrix}
 \text{Erwartungswert einer} \\
 \text{Gr }\!\!\ddot{\mathrm{o}}\!\!\text{ sse}\text{, bei der sich das System }
 \\
 \text{im Zustand }\left| {{\Psi }_{i}} \right\rangle \text{ befindet}
\end{smallmatrix}}} 
\end{align}

TeX (checked):

{\begin{aligned}&\left\langle {{O}_{S}}\right\rangle =\operatorname {Tr} \left(\rho {{O}_{s}}\right)=\underbrace {\sum \limits _{n}{\left\langle n\right|\rho {{O}_{s}}\left|n\right\rangle }} _{\begin{smallmatrix}n{\text{ vollst}}{\text{. System im}}\\{\text{Vielteilchenraum des }}\\{\text{Systems}}\end{smallmatrix}}\\&=\sum \limits _{n}{\left\langle n\right|\underbrace {\sum \limits _{i}{{{w}_{i}}\left|{{\Psi }_{i}}\right\rangle \left\langle {{\Psi }_{i}}\right|}} _{\rho }{{O}_{s}}\left|n\right\rangle }=\sum \limits _{i}{{{w}_{i}}\left\langle {{\Psi }_{i}}\right|\underbrace {\sum \limits _{n}{\left|n\right\rangle \left\langle n\right|}} _{1}}{{O}_{s}}\left|{{\Psi }_{i}}\right\rangle \\&=\sum \limits _{i}{{{w}_{i}}\underbrace {\left\langle {{\Psi }_{i}}\right|{{O}_{s}}\left|{{\Psi }_{i}}\right\rangle } _{\begin{smallmatrix}{\text{Erwartungswert einer}}\\{\text{Gr }}\!\!{\ddot {\mathrm {o} }}\!\!{\text{ sse}}{\text{, bei der sich das System }}\\{\text{im Zustand }}\left|{{\Psi }_{i}}\right\rangle {\text{ befindet}}\end{smallmatrix}}}\end{aligned}}

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\begin{aligned} ⟨ O_{S} ⟩ = Tr (ρ O_{s}) = \underset{\begin{matrix} n vollst . System im \\ Vielteilchenraum des \\ Systems \end{matrix}}{\underset{⏟}{\sum_{n} ⟨ n | ρ O_{s} | n ⟩}} \\ = \sum_{n} ⟨ n | \underset{ρ}{\underset{⏟}{\sum_{i} w_{i} | Ψ_{i} ⟩ ⟨ Ψ_{i} |}} O_{s} | n ⟩ = \sum_{i} w_{i} ⟨ Ψ_{i} | \underset{1}{\underset{⏟}{\sum_{n} | n ⟩ ⟨ n |}} O_{s} | Ψ_{i} ⟩ \\ = \sum_{i} w_{i} \underset{\begin{matrix} Erwartungswert einer \\ Gr \ddot{o} sse, bei der sich das System \\ im Zustand | Ψ_{i} ⟩ befindet \end{matrix}}{\underset{⏟}{⟨ Ψ_{i} | O_{s} | Ψ_{i} ⟩}} \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$O_{S}$

$ρ$

$O_{s}$

$n$

$n$

$ρ$

$O_{s}$

$n$

$n$

$n$

$n$

$i$

$w_{i}$

$Ψ_{i}$

$Ψ_{i}$

$ρ$

$O_{s}$

$n$

$i$

$w_{i}$

$Ψ_{i}$

$n$

$n$

$n$

$O_{s}$

$Ψ_{i}$

$i$

$w_{i}$

$Ψ_{i}$

$O_{s}$

$Ψ_{i}$

$\ddot{o}$

$Ψ_{i}$

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