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Display information for equation id:math.1666.66 on revision:1666
* Page found: Drehimpuls- Eigenzustände (eq math.1666.66)
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Hash: f8f1e184415df00ded95bcd1e1e38828
TeX (original user input):
\begin{align}
& {{b}_{\min }}^{2}+2n\hbar {{b}_{\min }}+{{n}^{2}}{{\hbar }^{2}}+\hbar \left( {{b}_{\min }}+n\hbar \right)={{b}_{\min }}^{2}-\hbar {{b}_{\min }} \\
& 2n\hbar {{b}_{\min }}+{{n}^{2}}{{\hbar }^{2}}+\hbar \left( 2{{b}_{\min }}+n\hbar \right)=0 \\
& \Rightarrow {{b}_{\min }}=-\frac{n(n+1){{\hbar }^{2}}}{2(n+1)\hbar }=-\frac{n}{2}\hbar =:-l\hbar \\
\end{align}
TeX (checked):
{\begin{aligned}&{{b}_{\min }}^{2}+2n\hbar {{b}_{\min }}+{{n}^{2}}{{\hbar }^{2}}+\hbar \left({{b}_{\min }}+n\hbar \right)={{b}_{\min }}^{2}-\hbar {{b}_{\min }}\\&2n\hbar {{b}_{\min }}+{{n}^{2}}{{\hbar }^{2}}+\hbar \left(2{{b}_{\min }}+n\hbar \right)=0\\&\Rightarrow {{b}_{\min }}=-{\frac {n(n+1){{\hbar }^{2}}}{2(n+1)\hbar }}=-{\frac {n}{2}}\hbar =:-l\hbar \\\end{aligned}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mn>2</mn><mi>n</mi><mi alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo stretchy="false">+</mo><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo stretchy="false">+</mo><mi>n</mi><mi alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mn>2</mn><mi>n</mi><mi alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo stretchy="false">+</mo><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo stretchy="false">+</mo><mi>n</mi><mi alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mo>min</mo></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo><msup><mi alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">+</mo><mn>1</mn><mo stretchy="false">)</mo><mi alternate="1">ℏ</mi></mrow></mrow></mfrac></mrow><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi alternate="1">ℏ</mi><mo stretchy="false">=</mo><mo stretchy="false">:</mo><mo stretchy="false">−</mo><mi>l</mi><mi alternate="1">ℏ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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