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Display information for equation id:math.2413.30 on revision:2413

* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2413.30)

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Quantenmechanische Gleichgewichtsverteilungen Eq: math.2413.30

Hash: 41ada87c02a9ecba7f5c46210f24759a

TeX (original user input):

\begin{align}
& \left\langle {\hat{M}} \right\rangle =\left\langle  \Psi  \right|\hat{M}\left| \Psi  \right\rangle =\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha   |  \Psi  \right\rangle \left\langle  \Psi  \right|\hat{M}\left| \alpha  \right\rangle =\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha  \right|{{{\hat{P}}}_{\Psi }}\hat{M}\left| \alpha  \right\rangle :=tr\left( {{{\hat{P}}}_{\Psi }}\hat{M} \right)=tr\left( \hat{M}{{{\hat{P}}}_{\Psi }} \right) \\
& tr\hat{X}:=\sum\limits_{\alpha }^{{}}{{}}\left\langle  \alpha  \right|\hat{X}\left| \alpha  \right\rangle  \\
\end{align}

TeX (checked):

{\begin{aligned}&\left\langle {\hat {M}}\right\rangle =\left\langle \Psi \right|{\hat {M}}\left|\Psi \right\rangle =\sum \limits _{\alpha }^{}{}\left\langle \alpha |\Psi \right\rangle \left\langle \Psi \right|{\hat {M}}\left|\alpha \right\rangle =\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|{{\hat {P}}_{\Psi }}{\hat {M}}\left|\alpha \right\rangle :=tr\left({{\hat {P}}_{\Psi }}{\hat {M}}\right)=tr\left({\hat {M}}{{\hat {P}}_{\Psi }}\right)\\&tr{\hat {X}}:=\sum \limits _{\alpha }^{}{}\left\langle \alpha \right|{\hat {X}}\left|\alpha \right\rangle \\\end{aligned}}

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MathML (4.145 KB / 497 B) :

\begin{aligned} ⟨ \hat{M} ⟩ = ⟨ Ψ | \hat{M} | Ψ ⟩ = \sum_{α}^{} ⟨ α | Ψ ⟩ ⟨ Ψ | \hat{M} | α ⟩ = \sum_{α}^{} ⟨ α | {\hat{P}}_{Ψ} \hat{M} | α ⟩ : = t r ({\hat{P}}_{Ψ} \hat{M}) = t r (\hat{M} {\hat{P}}_{Ψ}) \\ t r \hat{X} : = \sum_{α}^{} ⟨ α | \hat{X} | α ⟩ \end{aligned}

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Translations to Computer Algebra Systems

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Identifiers

$\hat{M}$

$Ψ$

$\hat{M}$

$Ψ$

$α$

$α$

$Ψ$

$Ψ$

$\hat{M}$

$α$

$α$

$α$

${\hat{P}}_{Ψ}$

$\hat{M}$

$α$

$t$

$r$

${\hat{P}}_{Ψ}$

$\hat{M}$

$t$

$r$

$\hat{M}$

${\hat{P}}_{Ψ}$

$t$

$r$

$\hat{X}$

$α$

$α$

$\hat{X}$

$α$

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