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Display information for equation id:math.1632.32 on revision:1632

* Page found: Eigenwerte und Eigenzustände von hermiteschen Operatoren (eq math.1632.32)

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\Rightarrow \left[ \hat{F},\hat{G} \right]\left| n \right\rangle =\hat{F}\hat{G}\left| n \right\rangle -\hat{G}\hat{F}\left| n \right\rangle =\hat{F}\hat{G}\left| n \right\rangle -{{F}_{n}}\hat{G}\left| n \right\rangle =0

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⇒ [ F ^ , G ^ ] ⁢ | n ⟩ = F ^ ⁢ G ^ ⁢ | n ⟩ - G ^ ⁢ F ^ ⁢ | n ⟩ = F ^ ⁢ G ^ ⁢ | n ⟩ - F n ⁢ G ^ ⁢ | n ⟩ = 0 ⇒ absent ^ 𝐹 ^ 𝐺 ket 𝑛 ^ 𝐹 ^ 𝐺 ket 𝑛 ^ 𝐺 ^ 𝐹 ket 𝑛 ^ 𝐹 ^ 𝐺 ket 𝑛 subscript 𝐹 𝑛 ^ 𝐺 ket 𝑛 0 {\displaystyle{\displaystyle\Rightarrow\left[\hat{F},\hat{G}\right]\left|n% \right\rangle=\hat{F}\hat{G}\left|n\right\rangle-\hat{G}\hat{F}\left|n\right% \rangle=\hat{F}\hat{G}\left|n\right\rangle-{{F}_{n}}\hat{G}\left|n\right% \rangle=0}}

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⇒[F^,G^]|n⟩=F^G^|n⟩−G^F^|n⟩=F^G^|n⟩−FnG^|n⟩=0

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