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Display information for equation id:math.971.54 on revision:971

* Page found: Übersicht:Thermodynamik (eq math.971.54)

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\left\langle {{{\hat{M}}}_{\alpha }} \right\rangle =\sum{{{P}_{i}}\left\langle \psi \left| {{M}_{\alpha }} \right|\psi  \right\rangle }=\operatorname{Tr}\left( \hat{\rho }{{{\hat{M}}}_{\alpha }} \right)

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MathML (7.942 KB / 1.367 KB) :

⟨ M ^ α ⟩ = ∑ P i ⁢ ⟨ ψ | M α | ψ ⟩ = Tr ⁡ ( ρ ^ ⁢ M ^ α ) delimited-⟨⟩ subscript ^ 𝑀 𝛼 subscript 𝑃 𝑖 quantum-operator-product 𝜓 subscript 𝑀 𝛼 𝜓 Tr ^ 𝜌 subscript ^ 𝑀 𝛼 {\displaystyle{\displaystyle\left\langle{{{\hat{M}}}_{\alpha}}\right\rangle=% \sum{{{P}_{i}}\left\langle\psi\left|{{M}_{\alpha}}\right|\psi\right\rangle}=% \operatorname{Tr}\left(\hat{\rho}{{{\hat{M}}}_{\alpha}}\right)}}

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⟨M^α⟩=∑Pi⟨ψ|Mα|ψ⟩=Tr⁡(ρ^M^α)

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