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Display information for equation id:math.1677.42 on revision:1677
* Page found: Kugelsymmetrische Potentiale (eq math.1677.42)
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Hash: af3f094a757da9e1a1c1e7823a26ef7f
TeX (original user input):
H\Psi (r,\vartheta ,\phi )=\frac{{{p}^{2}}}{2m}\Psi (r,\vartheta ,\phi )+V(r)\Psi (r,\vartheta ,\phi )=\frac{-{{\hbar }^{2}}}{2m}\frac{1}{r}\frac{{{\partial }^{2}}}{\partial {{r}^{2}}}\left( r\Psi \right)+\left[ \frac{{{L}^{2}}}{2m{{r}^{2}}}+V(r) \right]\Psi =E\Psi (r,\vartheta ,\phi )
TeX (checked):
H\Psi (r,\vartheta ,\phi )={\frac {{p}^{2}}{2m}}\Psi (r,\vartheta ,\phi )+V(r)\Psi (r,\vartheta ,\phi )={\frac {-{{\hbar }^{2}}}{2m}}{\frac {1}{r}}{\frac {{\partial }^{2}}{\partial {{r}^{2}}}}\left(r\Psi \right)+\left[{\frac {{L}^{2}}{2m{{r}^{2}}}}+V(r)\right]\Psi =E\Psi (r,\vartheta ,\phi )
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MathML (2.651 KB / 436 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>H</mi><mi mathvariant="normal">Ψ</mi><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>p</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">Ψ</mi><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</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><mi>m</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>r</mi><mi mathvariant="normal">Ψ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mi mathvariant="normal">Ψ</mi><mo>=</mo><mi>E</mi><mi mathvariant="normal">Ψ</mi><mo stretchy="false">(</mo><mi>r</mi><mo>,</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo></mstyle></mrow></math>
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