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Display information for equation id:math.2507.17 on revision:2507
* Page found: Das ideale Gas (eq math.2507.17)
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Hash: 8590fb2d9615cc9f5653d757c9f00d13
TeX (original user input):
{{e}^{-\Psi }}=Y=\exp \left( \frac{pV}{kT} \right)=\exp -\left( \frac{J(T,V,\mu )}{kT} \right)=\sum\limits_{N=0}^{\infty }{{}}\frac{1}{N!}\frac{1}{{{\hbar }^{3N}}}\int_{{{R}^{6N}}}^{{}}{{}}d{{\xi }_{N}}\exp \left( -\beta H-\alpha N \right)
TeX (checked):
{{e}^{-\Psi }}=Y=\exp \left({\frac {pV}{kT}}\right)=\exp -\left({\frac {J(T,V,\mu )}{kT}}\right)=\sum \limits _{N=0}^{\infty }{}{\frac {1}{N!}}{\frac {1}{{\hbar }^{3N}}}\int _{{R}^{6N}}^{}{}d{{\xi }_{N}}\exp \left(-\beta H-\alpha N\right)
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MathML (2.527 KB / 517 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mi mathvariant="normal">Ψ</mi></mrow></mrow></msup></mstyle><mo>=</mo><mi>Y</mi><mo>=</mo><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>V</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>exp</mi><mo>⁡</mo><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>J</mi><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>V</mi><mo>,</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>N</mi><mo>=</mo><mn>0</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover><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"><mi>N</mi><mi>!</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"><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>3</mn><mi>N</mi></mrow></mrow></msup></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>6</mn><mi>N</mi></mrow></mrow></msup></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mi>d</mi><msub><mi>ξ</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mi>exp</mi><mo>⁡</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mi>β</mi><mi>H</mi><mo>−</mo><mi>α</mi><mi>N</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></math>
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