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Display information for equation id:math.1677.79 on revision:1677

* Page found: Kugelsymmetrische Potentiale (eq math.1677.79)

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Kugelsymmetrische Potentiale Eq: math.1677.79

Hash: 7050f0bdaf325286b1716b5b750fed55

TeX (original user input):

\begin{align}

& H\Psi =\left( \frac{{{p}^{2}}}{2m}+V(r) \right)\Psi =\left( \frac{\left( \bar{r}\cdot \bar{p} \right)\left[ \left( \bar{r}\cdot \bar{p} \right)+\frac{\hbar }{i} \right]}{2m{{r}^{2}}}+\frac{{{L}^{2}}}{2m{{r}^{2}}}+V(r) \right)\Psi  \\

& =H\Psi =\frac{1}{2m}\left[ -\frac{{{\hbar }^{2}}}{r}\frac{{{\partial }^{2}}}{\partial {{r}^{2}}}\left( r\Psi  \right) \right]+\frac{{{L}^{2}}}{2m{{r}^{2}}}\Psi +V(r)\Psi  \\

& -\frac{{{\hbar }^{2}}}{r}\frac{{{\partial }^{2}}}{\partial {{r}^{2}}}\left( r\Psi  \right)={{p}_{r}}^{2} \\

\end{align}

TeX (checked):

{\begin{aligned}&H\Psi =\left({\frac {{p}^{2}}{2m}}+V(r)\right)\Psi =\left({\frac {\left({\bar {r}}\cdot {\bar {p}}\right)\left[\left({\bar {r}}\cdot {\bar {p}}\right)+{\frac {\hbar }{i}}\right]}{2m{{r}^{2}}}}+{\frac {{L}^{2}}{2m{{r}^{2}}}}+V(r)\right)\Psi \\&=H\Psi ={\frac {1}{2m}}\left[-{\frac {{\hbar }^{2}}{r}}{\frac {{\partial }^{2}}{\partial {{r}^{2}}}}\left(r\Psi \right)\right]+{\frac {{L}^{2}}{2m{{r}^{2}}}}\Psi +V(r)\Psi \\&-{\frac {{\hbar }^{2}}{r}}{\frac {{\partial }^{2}}{\partial {{r}^{2}}}}\left(r\Psi \right)={{p}_{r}}^{2}\\\end{aligned}}

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\begin{aligned} H Ψ = (\frac{p^{2}}{2 m} + V (r)) Ψ = (\frac{(\bar{r} \cdot \bar{p}) [(\bar{r} \cdot \bar{p}) + \frac{ℏ}{i}]}{2 m r^{2}} + \frac{L^{2}}{2 m r^{2}} + V (r)) Ψ \\ = H Ψ = \frac{1}{2 m} [- \frac{ℏ^{2}}{r} \frac{\partial^{2}}{\partial r^{2}} (r Ψ)] + \frac{L^{2}}{2 m r^{2}} Ψ + V (r) Ψ \\ - \frac{ℏ^{2}}{r} \frac{\partial^{2}}{\partial r^{2}} (r Ψ) = {p_{r}}^{2} \end{aligned}

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Identifiers

$H$

$Ψ$

$p$

$m$

$V$

$r$

$Ψ$

$\bar{r}$

$\bar{p}$

$\bar{r}$

$\bar{p}$

$i$

$m$

$r$

$L$

$m$

$r$

$V$

$r$

$Ψ$

$H$

$Ψ$

$m$

$r$

$r$

$r$

$Ψ$

$L$

$m$

$r$

$Ψ$

$V$

$r$

$Ψ$

$r$

$r$

$r$

$Ψ$

$p_{r}$

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