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Display information for equation id:math.1664.16 on revision:1664

* Page found: Drehimpuls- Eigenzustände (eq math.1664.16)

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Hash: fe156d601743522f26572415abbf9d42

TeX (original user input): 

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

TeX (checked): 

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

LaTeXML (experimental; uses MathML) rendering

MathML (14.477 KB / 2.039 KB) :

[ L ^ + , L ^ 3 ] ′′′ = [ L ^ 1 , L ^ 3 ] + i [ L ^ 2 , L ^ 3 ] = - i ℏ L ^ 2 - ℏ L ^ 1 = - ℏ ( L ^ 1 + i L ^ 2 ) fragments superscript fragments [ subscript ^ 𝐿 , subscript ^ 𝐿 3 ] ′′′ fragments [ subscript ^ 𝐿 1 , subscript ^ 𝐿 3 ] i fragments [ subscript ^ 𝐿 2 , subscript ^ 𝐿 3 ] i Planck-constant-over-2-pi subscript ^ 𝐿 2 Planck-constant-over-2-pi subscript ^ 𝐿 1 Planck-constant-over-2-pi fragments ( subscript ^ 𝐿 1 i subscript ^ 𝐿 2 ) {\displaystyle{{}^{\prime\prime\prime}\left[{{{\hat{L}}}_{+}},{{{\hat{L}}}_{3}% }\right]=\left[{{{\hat{L}}}_{1}},{{{\hat{L}}}_{3}}\right]+i\left[{{{\hat{L}}}_% {2}},{{{\hat{L}}}_{3}}\right]=-i\hbar{{\hat{L}}_{2}}-\hbar{{\hat{L}}_{1}}=-% \hbar\left({{{\hat{L}}}_{1}}+i{{{\hat{L}}}_{2}}\right)}} 
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    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{{}^{\prime\prime\prime}\left[{{{\hat{L}}}_{+}},{{{\hat{L}}}_{3}%
}\right]=\left[{{{\hat{L}}}_{1}},{{{\hat{L}}}_{3}}\right]+i\left[{{{\hat{L}}}_%
{2}},{{{\hat{L}}}_{3}}\right]=-i\hbar{{\hat{L}}_{2}}-\hbar{{\hat{L}}_{1}}=-%
\hbar\left({{{\hat{L}}}_{1}}+i{{{\hat{L}}}_{2}}\right)}}</annotation>
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</math>

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[L^+,L^3]=[L^1,L^3]+i[L^2,L^3]=−iℏL^2−ℏL^1=−ℏ(L^1+iL^2)
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Calculated based on the variables occurring on the entire Drehimpuls- Eigenzustände page

Identifiers

  • L^+
  • L^3
  • L^1
  • L^3
  • i
  • L^2
  • L^3
  • i
  • L^2
  • L^1
  • L^1
  • i
  • L^2

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