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Display information for equation id:math.1667.66 on revision:1667
* Page found: Drehimpuls- Eigenzustände (eq math.1667.66)
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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 class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mn>2</mn><mi>n</mi><mi data-mjx-alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mo>+</mo><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mo>+</mo><mi>n</mi><mi data-mjx-alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msup><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi data-mjx-alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mn>2</mn><mi>n</mi><mi data-mjx-alternate="1">ℏ</mi><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mo>+</mo><msup><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>+</mo><mi data-mjx-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"><mi>min</mi></mrow></msub><mo>+</mo><mi>n</mi><mi data-mjx-alternate="1">ℏ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msub><mi>b</mi><mrow data-mjx-texclass="ORD"><mi>min</mi></mrow></msub><mo>=</mo><mo>−</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>+</mo><mn>1</mn><mo stretchy="false">)</mo><msup><mi data-mjx-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>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi data-mjx-alternate="1">ℏ</mi></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</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 data-mjx-alternate="1">ℏ</mi><mo>=</mo><mi>:</mi><mo>−</mo><mi>l</mi><mi data-mjx-alternate="1">ℏ</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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