Jump to navigation Jump to search

General

Display information for equation id:math.1667.16 on revision:1667

* Page found: Drehimpuls- Eigenzustände (eq math.1667.16)

(force rerendering)

Occurrences on the following pages:

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)}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{{}^{\prime\prime\prime}\left[{{{\hat{L}}}_{+}},{{{\hat{L}}}_{3}%&#10;}\right]=\left[{{{\hat{L}}}_{1}},{{{\hat{L}}}_{3}}\right]+i\left[{{{\hat{L}}}_%&#10;{2}},{{{\hat{L}}}_{3}}\right]=-i\hbar{{\hat{L}}_{2}}-\hbar{{\hat{L}}_{1}}=-%&#10;\hbar\left({{{\hat{L}}}_{1}}+i{{{\hat{L}}}_{2}}\right)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mmultiscripts id="p1.1.m1.1.47" xref="p1.1.m1.1.47.cmml">
        <mrow id="p1.1.m1.1.47.4" xref="p1.1.m1.1.47.4.cmml">
          <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">[</mo>
          <msub id="p1.1.m1.1.47.2" xref="p1.1.m1.1.47.2.cmml">
            <mover accent="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
              <mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">L</mi>
              <mo stretchy="false" id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">^</mo>
            </mover>
            <mo id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">+</mo>
          </msub>
          <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">,</mo>
          <msub id="p1.1.m1.1.47.3" xref="p1.1.m1.1.47.3.cmml">
            <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
              <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">L</mi>
              <mo stretchy="false" id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">^</mo>
            </mover>
            <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">3</mn>
          </msub>
          <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">]</mo>
        </mrow>
        <mprescripts id="p1.1.m1.1.47a" xref="p1.1.m1.1.47.cmml"/>
        <none id="p1.1.m1.1.47b" xref="p1.1.m1.1.47.cmml"/>
        <mo id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">′′′</mo>
      </mmultiscripts>
      <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">=</mo>
      <mrow id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">[</mo>
        <msub id="p1.1.m1.1.48" xref="p1.1.m1.1.48.cmml">
          <mover accent="true" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
            <mi id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">,</mo>
        <msub id="p1.1.m1.1.49" xref="p1.1.m1.1.49.cmml">
          <mover accent="true" id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">
            <mi id="p1.1.m1.1.14.2" xref="p1.1.m1.1.14.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">3</mn>
        </msub>
        <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">]</mo>
      </mrow>
      <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">+</mo>
      <mi id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">i</mi>
      <mrow id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
        <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">[</mo>
        <msub id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml">
          <mover accent="true" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
            <mi id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">2</mn>
        </msub>
        <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">,</mo>
        <msub id="p1.1.m1.1.51" xref="p1.1.m1.1.51.cmml">
          <mover accent="true" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">
            <mi id="p1.1.m1.1.23.2" xref="p1.1.m1.1.23.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.23.1" xref="p1.1.m1.1.23.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">3</mn>
        </msub>
        <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">]</mo>
      </mrow>
      <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">=</mo>
      <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">-</mo>
      <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">i</mi>
      <mi mathvariant="normal" id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">ℏ</mi>
      <msub id="p1.1.m1.1.52" xref="p1.1.m1.1.52.cmml">
        <mover accent="true" id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">
          <mi id="p1.1.m1.1.30.2" xref="p1.1.m1.1.30.2.cmml">L</mi>
          <mo stretchy="false" id="p1.1.m1.1.30.1" xref="p1.1.m1.1.30.1.cmml">^</mo>
        </mover>
        <mn id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">2</mn>
      </msub>
      <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">-</mo>
      <mi mathvariant="normal" id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">ℏ</mi>
      <msub id="p1.1.m1.1.53" xref="p1.1.m1.1.53.cmml">
        <mover accent="true" id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">
          <mi id="p1.1.m1.1.34.2" xref="p1.1.m1.1.34.2.cmml">L</mi>
          <mo stretchy="false" id="p1.1.m1.1.34.1" xref="p1.1.m1.1.34.1.cmml">^</mo>
        </mover>
        <mn id="p1.1.m1.1.35.1" xref="p1.1.m1.1.35.1.cmml">1</mn>
      </msub>
      <mo id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">=</mo>
      <mo id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">-</mo>
      <mi mathvariant="normal" id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">ℏ</mi>
      <mrow id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
        <mo id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">(</mo>
        <msub id="p1.1.m1.1.54" xref="p1.1.m1.1.54.cmml">
          <mover accent="true" id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">
            <mi id="p1.1.m1.1.40.2" xref="p1.1.m1.1.40.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.40.1" xref="p1.1.m1.1.40.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.41.1" xref="p1.1.m1.1.41.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">+</mo>
        <mi id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">i</mi>
        <msub id="p1.1.m1.1.55" xref="p1.1.m1.1.55.cmml">
          <mover accent="true" id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">
            <mi id="p1.1.m1.1.44.2" xref="p1.1.m1.1.44.2.cmml">L</mi>
            <mo stretchy="false" id="p1.1.m1.1.44.1" xref="p1.1.m1.1.44.1.cmml">^</mo>
          </mover>
          <mn id="p1.1.m1.1.45.1" xref="p1.1.m1.1.45.1.cmml">2</mn>
        </msub>
        <mo id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">)</mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <apply id="p1.1.m1.1.47.cmml" xref="p1.1.m1.1.47">
          <csymbol cd="ambiguous" id="p1.1.m1.1.47.1.cmml" xref="p1.1.m1.1.47">superscript</csymbol>
          <cerror id="p1.1.m1.1.47.4.cmml" xref="p1.1.m1.1.47.4">
            <csymbol cd="ambiguous" id="p1.1.m1.1.47.4a.cmml" xref="p1.1.m1.1.47.4">fragments</csymbol>
            <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">[</ci>
            <apply id="p1.1.m1.1.47.2.cmml" xref="p1.1.m1.1.47.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.47.2.1.cmml" xref="p1.1.m1.1.47.2">subscript</csymbol>
              <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
                <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">^</ci>
                <ci id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">𝐿</ci>
              </apply>
              <plus id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1"/>
            </apply>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">,</ci>
            <apply id="p1.1.m1.1.47.3.cmml" xref="p1.1.m1.1.47.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.47.3.1.cmml" xref="p1.1.m1.1.47.3">subscript</csymbol>
              <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">^</ci>
                <ci id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">𝐿</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">3</cn>
            </apply>
            <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">]</ci>
          </cerror>
          <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">′′′</ci>
        </apply>
        <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
        <cerror id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
          <csymbol cd="ambiguous" id="p1.1.m1.1.1a.cmml" xref="p1.1.m1.1.1">fragments</csymbol>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">[</ci>
          <apply id="p1.1.m1.1.48.cmml" xref="p1.1.m1.1.48">
            <csymbol cd="ambiguous" id="p1.1.m1.1.48.1.cmml" xref="p1.1.m1.1.48">subscript</csymbol>
            <apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
              <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">^</ci>
              <ci id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">1</cn>
          </apply>
          <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">,</ci>
          <apply id="p1.1.m1.1.49.cmml" xref="p1.1.m1.1.49">
            <csymbol cd="ambiguous" id="p1.1.m1.1.49.1.cmml" xref="p1.1.m1.1.49">subscript</csymbol>
            <apply id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">
              <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">^</ci>
              <ci id="p1.1.m1.1.14.2.cmml" xref="p1.1.m1.1.14.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">3</cn>
          </apply>
          <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">]</ci>
        </cerror>
        <plus id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/>
        <csymbol cd="unknown" id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">i</csymbol>
        <cerror id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">
          <csymbol cd="ambiguous" id="p1.1.m1.1.4a.cmml" xref="p1.1.m1.1.4">fragments</csymbol>
          <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">[</ci>
          <apply id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">
            <csymbol cd="ambiguous" id="p1.1.m1.1.50.1.cmml" xref="p1.1.m1.1.50">subscript</csymbol>
            <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
              <ci id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">^</ci>
              <ci id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">,</ci>
          <apply id="p1.1.m1.1.51.cmml" xref="p1.1.m1.1.51">
            <csymbol cd="ambiguous" id="p1.1.m1.1.51.1.cmml" xref="p1.1.m1.1.51">subscript</csymbol>
            <apply id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">
              <ci id="p1.1.m1.1.23.1.cmml" xref="p1.1.m1.1.23.1">^</ci>
              <ci id="p1.1.m1.1.23.2.cmml" xref="p1.1.m1.1.23.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">3</cn>
          </apply>
          <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">]</ci>
        </cerror>
        <eq id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26"/>
        <minus id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27"/>
        <csymbol cd="unknown" id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">i</csymbol>
        <csymbol cd="latexml" id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">Planck-constant-over-2-pi</csymbol>
        <apply id="p1.1.m1.1.52.cmml" xref="p1.1.m1.1.52">
          <csymbol cd="ambiguous" id="p1.1.m1.1.52.1.cmml" xref="p1.1.m1.1.52">subscript</csymbol>
          <apply id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">
            <ci id="p1.1.m1.1.30.1.cmml" xref="p1.1.m1.1.30.1">^</ci>
            <ci id="p1.1.m1.1.30.2.cmml" xref="p1.1.m1.1.30.2">𝐿</ci>
          </apply>
          <cn type="integer" id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">2</cn>
        </apply>
        <minus id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32"/>
        <csymbol cd="latexml" id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">Planck-constant-over-2-pi</csymbol>
        <apply id="p1.1.m1.1.53.cmml" xref="p1.1.m1.1.53">
          <csymbol cd="ambiguous" id="p1.1.m1.1.53.1.cmml" xref="p1.1.m1.1.53">subscript</csymbol>
          <apply id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">
            <ci id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34.1">^</ci>
            <ci id="p1.1.m1.1.34.2.cmml" xref="p1.1.m1.1.34.2">𝐿</ci>
          </apply>
          <cn type="integer" id="p1.1.m1.1.35.1.cmml" xref="p1.1.m1.1.35.1">1</cn>
        </apply>
        <eq id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36"/>
        <minus id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37"/>
        <csymbol cd="latexml" id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38">Planck-constant-over-2-pi</csymbol>
        <cerror id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">
          <csymbol cd="ambiguous" id="p1.1.m1.1.7a.cmml" xref="p1.1.m1.1.7">fragments</csymbol>
          <ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">(</ci>
          <apply id="p1.1.m1.1.54.cmml" xref="p1.1.m1.1.54">
            <csymbol cd="ambiguous" id="p1.1.m1.1.54.1.cmml" xref="p1.1.m1.1.54">subscript</csymbol>
            <apply id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40">
              <ci id="p1.1.m1.1.40.1.cmml" xref="p1.1.m1.1.40.1">^</ci>
              <ci id="p1.1.m1.1.40.2.cmml" xref="p1.1.m1.1.40.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.41.1.cmml" xref="p1.1.m1.1.41.1">1</cn>
          </apply>
          <plus id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42"/>
          <csymbol cd="unknown" id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">i</csymbol>
          <apply id="p1.1.m1.1.55.cmml" xref="p1.1.m1.1.55">
            <csymbol cd="ambiguous" id="p1.1.m1.1.55.1.cmml" xref="p1.1.m1.1.55">subscript</csymbol>
            <apply id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">
              <ci id="p1.1.m1.1.44.1.cmml" xref="p1.1.m1.1.44.1">^</ci>
              <ci id="p1.1.m1.1.44.2.cmml" xref="p1.1.m1.1.44.2">𝐿</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">)</ci>
        </cerror>
      </cerror>
    </annotation-xml>
    <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>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (6.65 KB / 647 B) :

‴ [ 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 ) {\displaystyle '''\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)} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle '''\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)}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msup>
          <mi></mi>
          <mo>&#x2034;</mo>
        </msup>
        <mrow>
          <mo>[</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mo>+</mo>
                </mrow>
              </msub>
            </mrow>
            <mo>,</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>3</mn>
                </mrow>
              </msub>
            </mrow>
          </mrow>
          <mo>]</mo>
        </mrow>
        <mo>=</mo>
        <mrow>
          <mo>[</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>1</mn>
                </mrow>
              </msub>
            </mrow>
            <mo>,</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>3</mn>
                </mrow>
              </msub>
            </mrow>
          </mrow>
          <mo>]</mo>
        </mrow>
        <mo>+</mo>
        <mi>i</mi>
        <mrow>
          <mo>[</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msub>
            </mrow>
            <mo>,</mo>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>3</mn>
                </mrow>
              </msub>
            </mrow>
          </mrow>
          <mo>]</mo>
        </mrow>
        <mo>=</mo>
        <mo>&#x2212;<!-- − --></mo>
        <mi>i</mi>
        <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi>
        <mrow class="MJX-TeXAtom-ORD">
          <msub>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi>L</mi>
                  <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mn>2</mn>
            </mrow>
          </msub>
        </mrow>
        <mo>&#x2212;<!-- − --></mo>
        <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi>
        <mrow class="MJX-TeXAtom-ORD">
          <msub>
            <mrow class="MJX-TeXAtom-ORD">
              <mrow class="MJX-TeXAtom-ORD">
                <mover>
                  <mi>L</mi>
                  <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                </mover>
              </mrow>
            </mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mn>1</mn>
            </mrow>
          </msub>
        </mrow>
        <mo>=</mo>
        <mo>&#x2212;<!-- − --></mo>
        <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi>
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>1</mn>
                </mrow>
              </msub>
            </mrow>
            <mo>+</mo>
            <mi>i</mi>
            <mrow class="MJX-TeXAtom-ORD">
              <msub>
                <mrow class="MJX-TeXAtom-ORD">
                  <mrow class="MJX-TeXAtom-ORD">
                    <mover>
                      <mi>L</mi>
                      <mo stretchy="false">&#x005E;<!-- ^ --></mo>
                    </mover>
                  </mrow>
                </mrow>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msub>
            </mrow>
          </mrow>
          <mo>)</mo>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle '''\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>
  </semantics>
</math>

SVG (10.844 KB / 3.516 KB) :

{\displaystyle '''\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)}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Drehimpuls- Eigenzustände page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"