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Display information for equation id:math.1672.19 on revision:1672
* Page found: Ortsdarstellung des Bahndrehimpulses (eq math.1672.19)
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Hash: eacd9938542276a9c4c6822df74a9ea6
TeX (original user input):
{{\Psi }_{l,l-1}}(\bar{r})\propto \left\langle {\bar{r}} \right|{{\hat{L}}_{-}}\left| ll \right\rangle =\hbar {{e}^{i(l-1)\phi }}\left( -\frac{\partial }{\partial \vartheta }-l\cot \vartheta \right){{f}_{ll}}(r,\vartheta )=\hbar {{e}^{i(l-1)\phi }}{{\left( \sin \vartheta \right)}^{1-l}}\frac{\partial }{\partial \cos \vartheta }\left[ {{\left( \sin \vartheta \right)}^{l}}{{f}_{ll}}(r,\vartheta \right]
TeX (checked):
{{\Psi }_{l,l-1}}({\bar {r}})\propto \left\langle {\bar {r}}\right|{{\hat {L}}_{-}}\left|ll\right\rangle =\hbar {{e}^{i(l-1)\phi }}\left(-{\frac {\partial }{\partial \vartheta }}-l\cot \vartheta \right){{f}_{ll}}(r,\vartheta )=\hbar {{e}^{i(l-1)\phi }}{{\left(\sin \vartheta \right)}^{1-l}}{\frac {\partial }{\partial \cos \vartheta }}\left[{{\left(\sin \vartheta \right)}^{l}}{{f}_{ll}}(r,\vartheta \right]
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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"><msub><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mo>,</mo><mi>l</mi><mo>−</mo><mn>1</mn></mrow></mrow></msub></mstyle><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo stretchy="false">)</mo><mo>∝</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>L</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mo>−</mo></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>l</mi><mi>l</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo>=</mo><mi data-mjx-alternate="1">ℏ</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">(</mo><mi>l</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi>ϕ</mi></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>ϑ</mi></mrow></mrow></mfrac></mrow><mo>−</mo><mi>l</mi><mi>cot</mi><mo>⁡</mo><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mi>l</mi></mrow></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo stretchy="false">)</mo><mo>=</mo><mi data-mjx-alternate="1">ℏ</mi><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">(</mo><mi>l</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi>ϕ</mi></mrow></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mo>−</mo><mi>l</mi></mrow></mrow></msup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msup><msub><mi>f</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mi>l</mi></mrow></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow></mrow></math>
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