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Display information for equation id:math.2606.21 on revision:2606
* Page found: Prüfungsfragen:Quantenmechanik (eq math.2606.21)
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Hash: 8d2800aec14f8c489dbf7ca893ad1e9e
TeX (original user input):
\psi_k(\vec{r}) = \frac{1}{(2\pi)^{3/2}}e^{i\vec{k}\vec{r}} - \frac{2m}{4\pi\hbar^2}\int d^3\vec{r^{\prime}} \cdot \frac{e^{ik|\vec{r} - \vec{r^{\prime}}|}} {|\vec{r} - \vec{r^{\prime}}|} V(\vec{r^{\prime}}) \psi_k(\vec{r^{\prime}})
TeX (checked):
\psi _{k}({\vec {r}})={\frac {1}{(2\pi )^{3/2}}}e^{i{\vec {k}}{\vec {r}}}-{\frac {2m}{4\pi \hbar ^{2}}}\int d^{3}{\vec {r^{\prime }}}\cdot {\frac {e^{ik|{\vec {r}}-{\vec {r^{\prime }}}|}}{|{\vec {r}}-{\vec {r^{\prime }}}|}}V({\vec {r^{\prime }}})\psi _{k}({\vec {r^{\prime }}})
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MathML (3.302 KB / 469 B) :
<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>ψ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><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="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mn>2</mn><mi>π</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mo>/</mo><mn>2</mn></mrow></mrow></msup></mrow></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>k</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>→</mo></mover></mrow></mrow></mrow></mrow></msup><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mo texclass="OP">∫</mo><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>→</mo></mover></mrow></mrow><mo>⋅</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mo>|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>→</mo></mover></mrow></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>→</mo></mover></mrow></mrow><mo>|</mo></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>|</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>→</mo></mover></mrow></mrow><mo>−</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>→</mo></mover></mrow></mrow><mo>|</mo></mrow></mrow></mfrac></mrow><mi>V</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>→</mo></mover></mrow></mrow><mo stretchy="false">)</mo><msub><mi>ψ</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">′</mi></mrow></msup><mo>→</mo></mover></mrow></mrow><mo stretchy="false">)</mo></mstyle></mrow></math>
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