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Display information for equation id:math.1639.39 on revision:1639

* Page found: Die Quantisierung (eq math.1639.39)

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Hash: a183e9a2afc0089fe9f1985af75e3042

TeX (original user input): 

\begin{align}

& \left\langle  \Psi  \right|\hat{F}\left| \Psi  \right\rangle =\sum\limits_{n,n\acute{\ }}^{{}}{\left\langle  \Psi   |  n \right\rangle \left\langle  n \right|\hat{F}\left| n\acute{\ } \right\rangle \left\langle  n\acute{\ }  |  \Psi  \right\rangle } \\

& \left\langle  n \right|\hat{F}\left| n\acute{\ } \right\rangle ={{F}_{n}}{{\delta }_{nn\acute{\ }}} \\

& \Rightarrow \left\langle  \Psi  \right|\hat{F}\left| \Psi  \right\rangle =\sum\limits_{n}^{{}}{{{F}_{n}}{{\left| \left\langle  n | \Psi  \right\rangle  \right|}^{2}}} \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left\langle \Psi \right|{\hat {F}}\left|\Psi \right\rangle =\sum \limits _{n,n{\acute {\ }}}^{}{\left\langle \Psi |n\right\rangle \left\langle n\right|{\hat {F}}\left|n{\acute {\ }}\right\rangle \left\langle n{\acute {\ }}|\Psi \right\rangle }\\&\left\langle n\right|{\hat {F}}\left|n{\acute {\ }}\right\rangle ={{F}_{n}}{{\delta }_{nn{\acute {\ }}}}\\&\Rightarrow \left\langle \Psi \right|{\hat {F}}\left|\Psi \right\rangle =\sum \limits _{n}^{}{{{F}_{n}}{{\left|\left\langle n|\Psi \right\rangle \right|}^{2}}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (27.36 KB / 3.175 KB) :

⟨ Ψ | F ^ | Ψ ⟩ = ∑ n , n ⁢ ´ ⟨ Ψ | n ⟩ ⁢ ⟨ n | F ^ | n ⁢ ´ ⟩ ⁢ ⟨ n ⁢ ´ | Ψ ⟩ ⟨ n | F ^ | n ⁢ ´ ⟩ = F n ⁢ δ n ⁢ n ⁢ ´ ⇒ ⟨ Ψ | F ^ | Ψ ⟩ = ∑ n F n ⁢ | ⟨ n | Ψ ⟩ | 2 absent quantum-operator-product Ψ ^ 𝐹 Ψ subscript 𝑛 𝑛 ´ absent inner-product Ψ 𝑛 quantum-operator-product 𝑛 ^ 𝐹 𝑛 ´ absent inner-product 𝑛 ´ absent Ψ absent quantum-operator-product 𝑛 ^ 𝐹 𝑛 ´ absent subscript 𝐹 𝑛 subscript 𝛿 𝑛 𝑛 ´ absent absent ⇒ absent quantum-operator-product Ψ ^ 𝐹 Ψ subscript 𝑛 subscript 𝐹 𝑛 superscript inner-product 𝑛 Ψ 2 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\left\langle\Psi% \right|\hat{F}\left|\Psi\right\rangle=\sum\limits_{n,n\acute{\ }}{\left\langle% \Psi|n\right\rangle\left\langle n\right|\hat{F}\left|n\acute{\ }\right\rangle% \left\langle n\acute{\ }|\Psi\right\rangle}\\ \par&\displaystyle\left\langle n\right|\hat{F}\left|n\acute{\ }\right\rangle={% {F}_{n}}{{\delta}_{nn\acute{\ }}}\\ \par&\displaystyle\Rightarrow\left\langle\Psi\right|\hat{F}\left|\Psi\right% \rangle=\sum\limits_{n}{{{F}_{n}}{{\left|\left\langle n|\Psi\right\rangle% \right|}^{2}}}\\ \end{aligned}}}

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MathML (4.212 KB / 545 B) :

⟨Ψ|F^|Ψ⟩=∑n,n´⟨Ψ|n⟩⟨n|F^|n´⟩⟨n´|Ψ⟩⟨n|F^|n´⟩=Fnδnn´⇒⟨Ψ|F^|Ψ⟩=∑nFn|⟨n|Ψ⟩|2

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