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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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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}

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MathML (27.192 KB / 3.066 KB) :

⟨ M ^ ⟩ = ⟨ Ψ | M ^ | Ψ ⟩ = ∑ α ⟨ α | Ψ ⟩ ⁢ ⟨ Ψ | M ^ | α ⟩ = ∑ α ⟨ α | P ^ Ψ ⁢ M ^ | α ⟩ := t ⁢ r ⁢ ( P ^ Ψ ⁢ M ^ ) = t ⁢ r ⁢ ( M ^ ⁢ P ^ Ψ ) t ⁢ r ⁢ X ^ := ∑ α ⟨ α | X ^ | α ⟩ missing-subexpression delimited-⟨⟩ ^ 𝑀 quantum-operator-product Ψ ^ 𝑀 Ψ subscript 𝛼 inner-product 𝛼 Ψ quantum-operator-product Ψ ^ 𝑀 𝛼 subscript 𝛼 quantum-operator-product 𝛼 subscript ^ 𝑃 Ψ ^ 𝑀 𝛼 assign 𝑡 𝑟 subscript ^ 𝑃 Ψ ^ 𝑀 𝑡 𝑟 ^ 𝑀 subscript ^ 𝑃 Ψ missing-subexpression assign 𝑡 𝑟 ^ 𝑋 subscript 𝛼 quantum-operator-product 𝛼 ^ 𝑋 𝛼 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\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)\\ &\displaystyle tr\hat{X}:=\sum\limits_{\alpha}{{}}\left\langle\alpha\right|% \hat{X}\left|\alpha\right\rangle\\ \end{aligned}}}

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⟨M^⟩=⟨Ψ|M^|Ψ⟩=∑α⟨α|Ψ⟩⟨Ψ|M^|α⟩=∑α⟨α|P^ΨM^|α⟩:=tr(P^ΨM^)=tr(M^P^Ψ)trX^:=∑α⟨α|X^|α⟩

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