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* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.26)

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\Phi \left( x \right)=\sum\limits_{n=1}^{\infty }{\underbrace{\left\langle  {{\Psi }_{n}} | \Phi  \right\rangle }_{\text{Fourierkoeffizient}}{{\Psi }_{n}}\left( {\underline{x}} \right)\quad \forall \Phi \in {{\mathcal{H}}_{L}}}

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Φ ⁢ ( x ) = ∑ n = 1 ∞ ⟨ Ψ n | Φ ⟩ ⏟ Fourierkoeffizient ⁢ Ψ n ⁢ ( x ¯ )   ∀ Φ ∈ ℋ L formulae-sequence Φ 𝑥 superscript subscript 𝑛 1 subscript ⏟ inner-product subscript Ψ 𝑛 Φ Fourierkoeffizient subscript Ψ 𝑛 ¯ 𝑥 for-all Φ subscript ℋ 𝐿 {\displaystyle{\displaystyle\Phi\left(x\right)=\sum\limits_{n=1}^{\infty}{% \underbrace{\left\langle{{\Psi}_{n}}|\Phi\right\rangle}_{\text{% Fourierkoeffizient}}{{\Psi}_{n}}\left({\underline{x}}\right)\quad\forall\Phi% \in{{\mathcal{H}}_{L}}}}} 
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Φ ( x ) = ∑ n = 1 ∞ ⟨ Ψ n | Φ ⟩ ⏟ Fourierkoeffizient Ψ n ( x _ ) ∀ Φ ∈ H L {\displaystyle \Phi \left(x\right)=\sum \limits _{n=1}^{\infty }{\underbrace {\left\langle {{\Psi }_{n}}|\Phi \right\rangle } _{\text{Fourierkoeffizient}}{{\Psi }_{n}}\left({\underline {x}}\right)\quad \forall \Phi \in {{\mathcal {H}}_{L}}}} 
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{\displaystyle \Phi \left(x\right)=\sum \limits _{n=1}^{\infty }{\underbrace {\left\langle {{\Psi }_{n}}|\Phi \right\rangle } _{\text{Fourierkoeffizient}}{{\Psi }_{n}}\left({\underline {x}}\right)\quad \forall \Phi \in {{\mathcal {H}}_{L}}}}

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