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Display information for equation id:math.2232.29 on revision:2232

* Page found: Quantentheoretischer Zugang (eq math.2232.29)

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{{\Psi }_{B}}=\frac{1}{\sqrt{\underbrace{N}_{\begin{smallmatrix}
 \text{Teilchenzahl} \\
 \text{wg Normierung}
\end{smallmatrix}}!}}\frac{1}{\underbrace{\sqrt{\prod\limits_{k}^{K}{{{N}_{k}}!}}}_{\begin{smallmatrix}
  & \text{wenn nur die Orbitale }{{\varphi }_{k}} \\
 & k<N\text{ besetzt weil mehrer} \\
 & \text{Teilchen in einem Orbital sitzen} \\
 & \text{so steht }{{\text{N}}_{k}}\text{ f }\!\!\ddot{\mathrm{u}}\!\!\text{ r die Zahl der} \\
 & \text{Teilchen in dem Orbital} \\
\end{smallmatrix}}}\underbrace{\sum\limits_{P}{P\left( {{\varphi }_{{{n}_{1}}}}\left( {{x}_{1}} \right)\ldots {{\varphi }_{{{n}_{k}}}}\left( {{x}_{k}} \right)\ldots {{\varphi }_{{{n}_{N}}}}\left( {{x}_{N}} \right) \right)}}_{\text{Zumme   }\!\!\ddot{\mathrm{u}}\!\!\text{ ber alle Permutationen}}

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ΨB=1N⏟Teilchenzahlwg Normierung!1∏kKNk!⏟wenn nur die Orbitale φkk<N besetzt weil mehrerTeilchen in einem Orbital sitzenso steht Nk f u¨ r die Zahl derTeilchen in dem Orbital∑PP(φn1(x1)…φnk(xk)…φnN(xN))⏟Zumme u¨ ber alle Permutationen
<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">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>B</mi></mrow></msub></mstyle><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"><msqrt><mrow data-mjx-texclass="ORD"><munder><mrow data-mjx-texclass="OP"><munder><mi>N</mi><mo>&#x23DF;</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mtext>Teilchenzahl</mtext></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mtext>wg Normierung</mtext></mrow></mtd></mtr></mtable></mrow></mrow></munder><mi>!</mi></mrow></msqrt></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><munderover><mo form="prefix" texclass="OP">&#x220F;</mo><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow><mrow data-mjx-texclass="ORD"><mi>K</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><msub><mi>N</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mi>!</mi></mrow></mrow></msqrt></mrow><mo>&#x23DF;</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>wenn nur die Orbitale&#xA0;</mtext></mrow><msub><mi>&#x03C6;</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mi>k</mi><mo>&lt;</mo><mi>N</mi><mrow data-mjx-texclass="ORD"><mtext>&#xA0;besetzt weil mehrer</mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>Teilchen in einem Orbital sitzen</mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>so steht&#xA0;</mtext></mrow><msub><mrow data-mjx-texclass="ORD"><mtext>N</mtext></mrow><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mtext>&#xA0;f&#xA0;</mtext></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mtext>&#xA0;r die Zahl der</mtext></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mtext>Teilchen in dem Orbital</mtext></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mrow></munder></mrow></mfrac></mrow><munder><mrow data-mjx-texclass="OP"><munder><mrow data-mjx-texclass="ORD"><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>P</mi></mrow></munder><mrow data-mjx-texclass="ORD"><mi>P</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>&#x03C6;</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2026;</mo><msub><mi>&#x03C6;</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>k</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2026;</mo><msub><mi>&#x03C6;</mi><mrow data-mjx-texclass="ORD"><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mo>&#x23DF;</mo></munder></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>Zumme&#xA0;</mtext></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">u</mi></mrow><mo>¨</mo></mover></mrow></mrow><mspace width="-0.167em"></mspace><mspace width="-0.167em"></mspace><mrow data-mjx-texclass="ORD"><mtext>&#xA0;ber alle Permutationen</mtext></mrow></mrow></mrow></munder></mrow></math>

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