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Display information for equation id:math.1619.64 on revision:1619

* Page found: Zustandsvektoren im Hilbertraum (eq math.1619.64)

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TeX (original user input): 

\begin{align}
& \left\langle  \Phi  | \Psi  \right\rangle ={{\lambda }_{1}}\left\langle  \Phi  | {{\Psi }_{1}} \right\rangle +{{\lambda }_{2}}\left\langle  \Phi  | {{\Psi }_{2}} \right\rangle  \\
& \Rightarrow \left\langle  \Phi  | \Psi  \right\rangle *={{\lambda }_{1}}*\left\langle  \Phi  | {{\Psi }_{1}} \right\rangle *+{{\lambda }_{2}}*\left\langle  \Phi  | {{\Psi }_{2}} \right\rangle * \\
& \Rightarrow \left\langle  \Psi  | \Phi  \right\rangle ={{\lambda }_{1}}*\left\langle  {{\Psi }_{1}} | \Phi  \right\rangle +{{\lambda }_{2}}*\left\langle  {{\Psi }_{2}} | \Phi  \right\rangle  \\
& \Rightarrow \left\langle  \Psi  \right|={{\lambda }_{1}}*\left\langle  {{\Psi }_{1}} \right|+{{\lambda }_{2}}*\left\langle  {{\Psi }_{2}} \right| \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left\langle \Phi |\Psi \right\rangle ={{\lambda }_{1}}\left\langle \Phi |{{\Psi }_{1}}\right\rangle +{{\lambda }_{2}}\left\langle \Phi |{{\Psi }_{2}}\right\rangle \\&\Rightarrow \left\langle \Phi |\Psi \right\rangle *={{\lambda }_{1}}*\left\langle \Phi |{{\Psi }_{1}}\right\rangle *+{{\lambda }_{2}}*\left\langle \Phi |{{\Psi }_{2}}\right\rangle *\\&\Rightarrow \left\langle \Psi |\Phi \right\rangle ={{\lambda }_{1}}*\left\langle {{\Psi }_{1}}|\Phi \right\rangle +{{\lambda }_{2}}*\left\langle {{\Psi }_{2}}|\Phi \right\rangle \\&\Rightarrow \left\langle \Psi \right|={{\lambda }_{1}}*\left\langle {{\Psi }_{1}}\right|+{{\lambda }_{2}}*\left\langle {{\Psi }_{2}}\right|\\\end{aligned}}

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⟨ Φ | Ψ ⟩ = λ 1 ⁢ ⟨ Φ | Ψ 1 ⟩ + λ 2 ⁢ ⟨ Φ | Ψ 2 ⟩ ⇒ ⟨ Φ | Ψ ⟩ * = λ 1 * ⟨ Φ | Ψ 1 ⟩ * + λ 2 * ⟨ Φ | Ψ 2 ⟩ * ⇒ ⟨ Ψ | Φ ⟩ = λ 1 * ⟨ Ψ 1 | Φ ⟩ + λ 2 * ⟨ Ψ 2 | Φ ⟩ ⇒ ⟨ Ψ | = λ 1 * ⟨ Ψ 1 | + λ 2 * ⟨ Ψ 2 | missing-subexpression inner-product Φ Ψ subscript 𝜆 1 inner-product Φ subscript Ψ 1 subscript 𝜆 2 inner-product Φ subscript Ψ 2 missing-subexpression fragments ⇒ fragments ⟨ Φ | Ψ ⟩ subscript 𝜆 1 fragments ⟨ Φ | subscript Ψ 1 ⟩ subscript 𝜆 2 fragments ⟨ Φ | subscript Ψ 2 ⟩ missing-subexpression ⇒ absent inner-product Ψ Φ subscript 𝜆 1 inner-product subscript Ψ 1 Φ subscript 𝜆 2 inner-product subscript Ψ 2 Φ missing-subexpression ⇒ absent bra Ψ subscript 𝜆 1 bra subscript Ψ 1 subscript 𝜆 2 bra subscript Ψ 2 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\left\langle\Phi|% \Psi\right\rangle={{\lambda}_{1}}\left\langle\Phi|{{\Psi}_{1}}\right\rangle+{{% \lambda}_{2}}\left\langle\Phi|{{\Psi}_{2}}\right\rangle\\ &\displaystyle\Rightarrow\left\langle\Phi|\Psi\right\rangle*={{\lambda}_{1}}*% \left\langle\Phi|{{\Psi}_{1}}\right\rangle*+{{\lambda}_{2}}*\left\langle\Phi|{% {\Psi}_{2}}\right\rangle*\\ &\displaystyle\Rightarrow\left\langle\Psi|\Phi\right\rangle={{\lambda}_{1}}*% \left\langle{{\Psi}_{1}}|\Phi\right\rangle+{{\lambda}_{2}}*\left\langle{{\Psi}% _{2}}|\Phi\right\rangle\\ &\displaystyle\Rightarrow\left\langle\Psi\right|={{\lambda}_{1}}*\left\langle{% {\Psi}_{1}}\right|+{{\lambda}_{2}}*\left\langle{{\Psi}_{2}}\right|\\ \end{aligned}}}

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⟨Φ|Ψ⟩=λ1⟨Φ|Ψ1⟩+λ2⟨Φ|Ψ2⟩⇒⟨Φ|Ψ⟩*=λ1*⟨Φ|Ψ1⟩*+λ2*⟨Φ|Ψ2⟩*⇒⟨Ψ|Φ⟩=λ1*⟨Ψ1|Φ⟩+λ2*⟨Ψ2|Φ⟩⇒⟨Ψ|=λ1*⟨Ψ1|+λ2*⟨Ψ2|

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