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Display information for equation id:math.1621.27 on revision:1621

* Page found: Operatoren im Hilbertraum (eq math.1621.27)

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\int_{-\infty }^{\infty }{dx}\phi {{*}_{m}}(x){{\phi }_{n}}(x)=\int_{-\infty }^{\infty }{dx}\left\langle  m | x \right\rangle \left\langle  x | n \right\rangle =\left\langle  m | n \right\rangle ={{\delta }_{mn}}

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∫ - ∞ ∞ 𝑑 x ⁢ ϕ * m ( x ) ⁢ ϕ n ⁢ ( x ) = ∫ - ∞ ∞ 𝑑 x ⁢ ⟨ m | x ⟩ ⁢ ⟨ x | n ⟩ = ⟨ m | n ⟩ = δ m ⁢ n superscript subscript subscript 𝑚 differential-d 𝑥 italic-ϕ 𝑥 subscript italic-ϕ 𝑛 𝑥 superscript subscript differential-d 𝑥 inner-product 𝑚 𝑥 inner-product 𝑥 𝑛 inner-product 𝑚 𝑛 subscript 𝛿 𝑚 𝑛 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}{dx}\phi{{*}_{m}}(x){{\phi}% _{n}}(x)=\int_{-\infty}^{\infty}{dx}\left\langle m|x\right\rangle\left\langle x% |n\right\rangle=\left\langle m|n\right\rangle={{\delta}_{mn}}}}

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∫−∞∞dxϕ*m(x)ϕn(x)=∫−∞∞dx⟨m|x⟩⟨x|n⟩=⟨m|n⟩=δmn

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