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Display information for equation id:math.1613.89 on revision:1613

* Page found: Zustandsvektoren im Hilbertraum (eq math.1613.89)

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Zustandsvektoren im Hilbertraum Eq: math.1619.89

Hash: 913a8e5dc9e76dabd09ffd8ea9c23302

TeX (original user input):

\left\langle  \Psi  | {\bar{r}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p\left\langle  \Psi  | {\bar{p}} \right\rangle }\left\langle  {\bar{p}} | {\bar{r}} \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p}\tilde{\Psi }(\bar{p})*{{\left( 2\pi \hbar  \right)}^{-\tfrac{3}{2}}}{{e}^{-\frac{i}{\hbar }\bar{p}\bar{r}}}=\left\langle  {\bar{r}} | \Psi  \right\rangle *=\Psi (\bar{r})*

TeX (checked):

\left\langle \Psi |{\bar {r}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}p\left\langle \Psi |{\bar {p}}\right\rangle }\left\langle {\bar {p}}|{\bar {r}}\right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}p}{\tilde {\Psi }}({\bar {p}})*{{\left(2\pi \hbar \right)}^{-{\tfrac {3}{2}}}}{{e}^{-{\frac {i}{\hbar }}{\bar {p}}{\bar {r}}}}=\left\langle {\bar {r}}|\Psi \right\rangle *=\Psi ({\bar {r}})*

LaTeXML (experimental; uses MathML) rendering

MathML (18.354 KB / 2.621 KB) :

{\displaystyle{\displaystyle\left\langle\Psi|{\bar{r}}\right\rangle=\int_{{{R}% ^{3}}}{{{d}^{3}}p\left\langle\Psi|{\bar{p}}\right\rangle}\left\langle{\bar{p}}% |{\bar{r}}\right\rangle=\int_{{{R}^{3}}}{{{d}^{3}}p}\tilde{\Psi}(\bar{p})*{{% \left(2\pi\hbar\right)}^{-\tfrac{3}{2}}}{{e}^{-\frac{i}{\hbar}\bar{p}\bar{r}}}% =\left\langle{\bar{r}}|\Psi\right\rangle*=\Psi(\bar{r})*}}

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    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle\left\langle\Psi|{\bar{r}}\right\rangle=\int_{{{R}%
^{3}}}{{{d}^{3}}p\left\langle\Psi|{\bar{p}}\right\rangle}\left\langle{\bar{p}}%
|{\bar{r}}\right\rangle=\int_{{{R}^{3}}}{{{d}^{3}}p}\tilde{\Psi}(\bar{p})*{{%
\left(2\pi\hbar\right)}^{-\tfrac{3}{2}}}{{e}^{-\frac{i}{\hbar}\bar{p}\bar{r}}}%
=\left\langle{\bar{r}}|\Psi\right\rangle*=\Psi(\bar{r})*}}</annotation>
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</math>

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MathML (3.625 KB / 518 B) :

⟨ Ψ | \bar{r} ⟩ = \int_{R^{3}}^{} d^{3} p ⟨ Ψ | \bar{p} ⟩ ⟨ \bar{p} | \bar{r} ⟩ = \int_{R^{3}}^{} d^{3} p \tilde{Ψ} (\bar{p}) * {(2 π ℏ)}^{- \frac{3}{2}} e^{- \frac{i}{ℏ} \bar{p} \bar{r}} = ⟨ \bar{r} | Ψ ⟩ * = Ψ (\bar{r}) *

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Identifiers

$Ψ$

$\bar{r}$

$R$

$p$

$Ψ$

$\bar{p}$

$\bar{p}$

$\bar{r}$

$R$

$p$

$\tilde{Ψ}$

$\bar{p}$

$π$

$e$

$i$

$\bar{p}$

$\bar{r}$

$\bar{r}$

$Ψ$

$Ψ$

$\bar{r}$

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