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Display information for equation id:math.1622.29 on revision:1622

* Page found: Operatoren im Hilbertraum (eq math.1622.29)

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Hash: ef00108384b1730b9d2a7e8e410f0c4c

TeX (original user input):

\begin{align}

& \left\langle  x | \Psi  \right\rangle =\Psi (x)=\sum\limits_{n=0}^{\infty }{{}}{{c}_{n}}{{\phi }_{n}}(x)=\sum\limits_{n=0}^{\infty }{{}}\left\langle  n | \Psi  \right\rangle \left\langle  x | n \right\rangle  \\

& \Rightarrow \sum\limits_{n=0}^{\infty }{{}}\left| n \right\rangle \left\langle  n \right|=1\  \\

\end{align}

TeX (checked):

{\begin{aligned}&\left\langle x|\Psi \right\rangle =\Psi (x)=\sum \limits _{n=0}^{\infty }{}{{c}_{n}}{{\phi }_{n}}(x)=\sum \limits _{n=0}^{\infty }{}\left\langle n|\Psi \right\rangle \left\langle x|n\right\rangle \\&\Rightarrow \sum \limits _{n=0}^{\infty }{}\left|n\right\rangle \left\langle n\right|=1\ \\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (19.843 KB / 2.404 KB) :

x | Ψ = Ψ ( x ) = n = 0 c n ϕ n ( x ) = n = 0 n | Ψ x | n n = 0 | n n | = 1 absent inner-product 𝑥 Ψ Ψ 𝑥 superscript subscript 𝑛 0 subscript 𝑐 𝑛 subscript italic-ϕ 𝑛 𝑥 superscript subscript 𝑛 0 inner-product 𝑛 Ψ inner-product 𝑥 𝑛 absent absent superscript subscript 𝑛 0 ket 𝑛 bra 𝑛 1 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\left\langle x|% \Psi\right\rangle=\Psi(x)=\sum\limits_{n=0}^{\infty}{{}}{{c}_{n}}{{\phi}_{n}}(% x)=\sum\limits_{n=0}^{\infty}{{}}\left\langle n|\Psi\right\rangle\left\langle x% |n\right\rangle\\ \par&\displaystyle\Rightarrow\sum\limits_{n=0}^{\infty}{{}}\left|n\right% \rangle\left\langle n\right|=1\\ \par\end{aligned}}}

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MathML (2.355 KB / 477 B) :

x|Ψ=Ψ(x)=n=0cnϕn(x)=n=0n|Ψx|nn=0|nn|=1

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