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Display information for equation id:math.1677.0 on revision:1677

* Page found: Kugelsymmetrische Potentiale (eq math.1677.0)

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Hash: 1197da911db4844d82f94eeec831ad12

TeX (original user input): 

\begin{align}

& \left[ {{{\hat{L}}}_{3}},{{{\hat{r}}}_{1}} \right]=\left[ \left( {{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}}-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}} \right),{{{\hat{r}}}_{1}} \right]=-{{{\hat{r}}}_{2}}\left[ {{{\hat{p}}}_{1}},{{{\hat{r}}}_{1}} \right]=i\hbar {{{\hat{r}}}_{2}} \\

& \left[ {{{\hat{L}}}_{3}},{{{\hat{r}}}_{2}} \right]=\left[ \left( {{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}}-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}} \right),{{{\hat{r}}}_{2}} \right]={{{\hat{r}}}_{1}}\left[ {{{\hat{p}}}_{2}},{{{\hat{r}}}_{2}} \right]=-i\hbar {{{\hat{r}}}_{1}} \\

& \left[ {{{\hat{L}}}_{3}},{{{\hat{r}}}_{3}} \right]=\left[ \left( {{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}}-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}} \right),{{{\hat{r}}}_{3}} \right]=0 \\

\end{align}

TeX (checked): 

{\begin{aligned}&\left[{{\hat {L}}_{3}},{{\hat {r}}_{1}}\right]=\left[\left({{\hat {r}}_{1}}{{\hat {p}}_{2}}-{{\hat {r}}_{2}}{{\hat {p}}_{1}}\right),{{\hat {r}}_{1}}\right]=-{{\hat {r}}_{2}}\left[{{\hat {p}}_{1}},{{\hat {r}}_{1}}\right]=i\hbar {{\hat {r}}_{2}}\\&\left[{{\hat {L}}_{3}},{{\hat {r}}_{2}}\right]=\left[\left({{\hat {r}}_{1}}{{\hat {p}}_{2}}-{{\hat {r}}_{2}}{{\hat {p}}_{1}}\right),{{\hat {r}}_{2}}\right]={{\hat {r}}_{1}}\left[{{\hat {p}}_{2}},{{\hat {r}}_{2}}\right]=-i\hbar {{\hat {r}}_{1}}\\&\left[{{\hat {L}}_{3}},{{\hat {r}}_{3}}\right]=\left[\left({{\hat {r}}_{1}}{{\hat {p}}_{2}}-{{\hat {r}}_{2}}{{\hat {p}}_{1}}\right),{{\hat {r}}_{3}}\right]=0\\\end{aligned}}

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MathML (53.443 KB / 4.972 KB) :

[ L ^ 3 , r ^ 1 ] = [ ( r ^ 1 ⁢ p ^ 2 - r ^ 2 ⁢ p ^ 1 ) , r ^ 1 ] = - r ^ 2 ⁢ [ p ^ 1 , r ^ 1 ] = i ⁢ ℏ ⁢ r ^ 2 [ L ^ 3 , r ^ 2 ] = [ ( r ^ 1 ⁢ p ^ 2 - r ^ 2 ⁢ p ^ 1 ) , r ^ 2 ] = r ^ 1 ⁢ [ p ^ 2 , r ^ 2 ] = - i ⁢ ℏ ⁢ r ^ 1 [ L ^ 3 , r ^ 3 ] = [ ( r ^ 1 ⁢ p ^ 2 - r ^ 2 ⁢ p ^ 1 ) , r ^ 3 ] = 0 absent subscript ^ 𝐿 3 subscript ^ 𝑟 1 subscript ^ 𝑟 1 subscript ^ 𝑝 2 subscript ^ 𝑟 2 subscript ^ 𝑝 1 subscript ^ 𝑟 1 subscript ^ 𝑟 2 subscript ^ 𝑝 1 subscript ^ 𝑟 1 𝑖 Planck-constant-over-2-pi subscript ^ 𝑟 2 absent subscript ^ 𝐿 3 subscript ^ 𝑟 2 subscript ^ 𝑟 1 subscript ^ 𝑝 2 subscript ^ 𝑟 2 subscript ^ 𝑝 1 subscript ^ 𝑟 2 subscript ^ 𝑟 1 subscript ^ 𝑝 2 subscript ^ 𝑟 2 𝑖 Planck-constant-over-2-pi subscript ^ 𝑟 1 absent subscript ^ 𝐿 3 subscript ^ 𝑟 3 subscript ^ 𝑟 1 subscript ^ 𝑝 2 subscript ^ 𝑟 2 subscript ^ 𝑝 1 subscript ^ 𝑟 3 0 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle\left[{{{\hat{L}% }}_{3}},{{{\hat{r}}}_{1}}\right]=\left[\left({{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}% }-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}}\right),{{{\hat{r}}}_{1}}\right]=-{{{\hat{% r}}}_{2}}\left[{{{\hat{p}}}_{1}},{{{\hat{r}}}_{1}}\right]=i\hbar{{{\hat{r}}}_{% 2}}\\ \par&\displaystyle\left[{{{\hat{L}}}_{3}},{{{\hat{r}}}_{2}}\right]=\left[\left% ({{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}}-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}}\right),% {{{\hat{r}}}_{2}}\right]={{{\hat{r}}}_{1}}\left[{{{\hat{p}}}_{2}},{{{\hat{r}}}% _{2}}\right]=-i\hbar{{{\hat{r}}}_{1}}\\ \par&\displaystyle\left[{{{\hat{L}}}_{3}},{{{\hat{r}}}_{3}}\right]=\left[\left% ({{{\hat{r}}}_{1}}{{{\hat{p}}}_{2}}-{{{\hat{r}}}_{2}}{{{\hat{p}}}_{1}}\right),% {{{\hat{r}}}_{3}}\right]=0\\ \par\end{aligned}}}

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MathML (6.825 KB / 476 B) :

[L^3,r^1]=[(r^1p^2−r^2p^1),r^1]=−r^2[p^1,r^1]=iℏr^2[L^3,r^2]=[(r^1p^2−r^2p^1),r^2]=r^1[p^2,r^2]=−iℏr^1[L^3,r^3]=[(r^1p^2−r^2p^1),r^3]=0

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Calculated based on the variables occurring on the entire Kugelsymmetrische Potentiale page

Identifiers

  • L^3
  • r^1
  • r^1
  • p^2
  • r^2
  • p^1
  • r^1
  • r^2
  • p^1
  • r^1
  • i
  • r^2
  • L^3
  • r^2
  • r^1
  • p^2
  • r^2
  • p^1
  • r^2
  • r^1
  • p^2
  • r^2
  • i
  • r^1
  • L^3
  • r^3
  • r^1
  • p^2
  • r^2
  • p^1
  • r^3

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