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Display information for equation id:math.1622.11 on revision:1622

* Page found: Operatoren im Hilbertraum (eq math.1622.11)

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\left\langle  {\bar{r}} | \Phi  \right\rangle =\left\langle  {\bar{r}} \right|\hat{F}\left| \Psi  \right\rangle =\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\left| \bar{r}\acute{\ } \right\rangle \left\langle  {\bar{r}} \right|\hat{F}\left| \Psi  \right\rangle \left\langle  \bar{r}\acute{\ } \right|=}\int_{{}}^{{}}{{{d}^{3}}r\acute{\ }\left\langle  {\bar{r}} \right|\hat{F}\left| \bar{r}\acute{\ } \right\rangle \left\langle  \bar{r}\acute{\ }  |  \Psi  \right\rangle }

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⟨ r ¯ | Φ ⟩ = ⟨ r ¯ | F ^ | Ψ ⟩ = ∫ d 3 ⁢ r ⁢ ´ ⁢ | r ¯ ⁢ ´ ⟩ ⁢ ⟨ r ¯ | F ^ | Ψ ⟩ ⁢ ⟨ r ¯ ⁢ ´ | = ∫ d 3 ⁢ r ⁢ ´ ⁢ ⟨ r ¯ | F ^ | r ¯ ⁢ ´ ⟩ ⁢ ⟨ r ¯ ⁢ ´ | Ψ ⟩ inner-product ¯ 𝑟 Φ quantum-operator-product ¯ 𝑟 ^ 𝐹 Ψ superscript 𝑑 3 𝑟 ´ absent ket ¯ 𝑟 ´ absent quantum-operator-product ¯ 𝑟 ^ 𝐹 Ψ bra ¯ 𝑟 ´ absent superscript 𝑑 3 𝑟 ´ absent quantum-operator-product ¯ 𝑟 ^ 𝐹 ¯ 𝑟 ´ absent inner-product ¯ 𝑟 ´ absent Ψ {\displaystyle{\displaystyle\left\langle{\bar{r}}|\Phi\right\rangle=\left% \langle{\bar{r}}\right|\hat{F}\left|\Psi\right\rangle=\int{{{d}^{3}}r\acute{\ % }\left|\bar{r}\acute{\ }\right\rangle\left\langle{\bar{r}}\right|\hat{F}\left|% \Psi\right\rangle\left\langle\bar{r}\acute{\ }\right|=}\int{{{d}^{3}}r\acute{% \ }\left\langle{\bar{r}}\right|\hat{F}\left|\bar{r}\acute{\ }\right\rangle% \left\langle\bar{r}\acute{\ }|\Psi\right\rangle}}}

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⟨r¯|Φ⟩=⟨r¯|F^|Ψ⟩=∫d3r´|r¯´⟩⟨r¯|F^|Ψ⟩⟨r¯´|=∫d3r´⟨r¯|F^|r¯´⟩⟨r¯´|Ψ⟩

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