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Display information for equation id:math.1618.80 on revision:1618

* Page found: Zustandsvektoren im Hilbertraum (eq math.1618.80)

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Zustandsvektoren im Hilbertraum Eq: math.1619.80

Hash: b961928c50b14f447c8289cc37c2d069

TeX (original user input):

\begin{align}
& \Psi (\bar{r})=\left\langle  {\bar{r}} | \Psi  \right\rangle =\frac{1}{{{\left( 2\pi \hbar  \right)}^{\tfrac{3}{2}}}}\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p{{e}^{\frac{i}{\hbar }\bar{p}\bar{r}}}}\left\langle  {\bar{p}} | \Psi  \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}p\left\langle  {\bar{r}} | {\bar{p}} \right\rangle }\left\langle  {\bar{p}} | \Psi  \right\rangle  \\
& \tilde{\Psi }(\bar{p})=\left\langle  {\bar{p}} | \Psi  \right\rangle =\frac{1}{{{\left( 2\pi \hbar  \right)}^{\tfrac{3}{2}}}}\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r{{e}^{-\frac{i}{\hbar }\bar{p}\bar{r}}}}\left\langle  {\bar{r}} | \Psi  \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r\left\langle  {\bar{r}} | {\bar{p}} \right\rangle *}\left\langle  {\bar{r}} | \Psi  \right\rangle =\int_{{{R}^{3}}}^{{}}{{{d}^{3}}r\left\langle  {\bar{p}} | {\bar{r}} \right\rangle }\left\langle  {\bar{r}} | \Psi  \right\rangle  \\ 

\end{align}

TeX (checked):

{\begin{aligned}&\Psi ({\bar {r}})=\left\langle {\bar {r}}|\Psi \right\rangle ={\frac {1}{{\left(2\pi \hbar \right)}^{\tfrac {3}{2}}}}\int _{{R}^{3}}^{}{{{d}^{3}}p{{e}^{{\frac {i}{\hbar }}{\bar {p}}{\bar {r}}}}}\left\langle {\bar {p}}|\Psi \right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}p\left\langle {\bar {r}}|{\bar {p}}\right\rangle }\left\langle {\bar {p}}|\Psi \right\rangle \\&{\tilde {\Psi }}({\bar {p}})=\left\langle {\bar {p}}|\Psi \right\rangle ={\frac {1}{{\left(2\pi \hbar \right)}^{\tfrac {3}{2}}}}\int _{{R}^{3}}^{}{{{d}^{3}}r{{e}^{-{\frac {i}{\hbar }}{\bar {p}}{\bar {r}}}}}\left\langle {\bar {r}}|\Psi \right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}r\left\langle {\bar {r}}|{\bar {p}}\right\rangle *}\left\langle {\bar {r}}|\Psi \right\rangle =\int _{{R}^{3}}^{}{{{d}^{3}}r\left\langle {\bar {p}}|{\bar {r}}\right\rangle }\left\langle {\bar {r}}|\Psi \right\rangle \\\end{aligned}}

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\begin{matrix} Ψ (\bar{r}) = ⟨ \bar{r} | Ψ ⟩ = \frac{1}{{(2 π ℏ)}^{\frac{3}{2}}} \int_{R^{3}}^{} d^{3} p e^{\frac{i}{ℏ} \bar{p} \bar{r}} ⟨ \bar{p} | Ψ ⟩ = \int_{R^{3}}^{} d^{3} p ⟨ \bar{r} | \bar{p} ⟩ ⟨ \bar{p} | Ψ ⟩ \\ \tilde{Ψ} (\bar{p}) = ⟨ \bar{p} | Ψ ⟩ = \frac{1}{{(2 π ℏ)}^{\frac{3}{2}}} \int_{R^{3}}^{} d^{3} r e^{- \frac{i}{ℏ} \bar{p} \bar{r}} ⟨ \bar{r} | Ψ ⟩ = \int_{R^{3}}^{} d^{3} r ⟨ \bar{r} | \bar{p} ⟩ * ⟨ \bar{r} | Ψ ⟩ = \int_{R^{3}}^{} d^{3} r ⟨ \bar{p} | \bar{r} ⟩ ⟨ \bar{r} | Ψ ⟩ \end{matrix}

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Identifiers

$Ψ$

$\bar{r}$

$\bar{r}$

$Ψ$

$π$

$R$

$p$

$e$

$i$

$\bar{p}$

$\bar{r}$

$\bar{p}$

$Ψ$

$R$

$p$

$\bar{r}$

$\bar{p}$

$\bar{p}$

$Ψ$

$\tilde{Ψ}$

$\bar{p}$

$\bar{p}$

$Ψ$

$π$

$R$

$r$

$e$

$i$

$\bar{p}$

$\bar{r}$

$\bar{r}$

$Ψ$

$R$

$r$

$\bar{r}$

$\bar{p}$

$\bar{r}$

$Ψ$

$R$

$r$

$\bar{p}$

$\bar{r}$

$\bar{r}$

$Ψ$

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