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Display information for equation id:math.1717.22 on revision:1717

* Page found: Identische Teilchen: Spin und Statistik (eq math.1717.22)

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Identische Teilchen: Spin und Statistik Eq: math.1720.22

Hash: e7e96d96aba145c7dfd7ecda660c0b9f

TeX (original user input):

\begin{align}

& {{\left| {{{\hat{p}}}_{\left( ij \right)}}\Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t) \right|}^{2}}={{\left| \Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t) \right|}^{2}}=1={{\left| {{\lambda }_{ij}}\Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t) \right|}^{2}} \\
& \Rightarrow {{\left| {{\lambda }_{ij}} \right|}^{2}}=1 \\
& \Rightarrow {{\lambda }_{ij}}=\pm 1 \\
\end{align}

TeX (checked):

{\begin{aligned}&{{\left|{{\hat {p}}_{\left(ij\right)}}\Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t)\right|}^{2}}={{\left|\Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t)\right|}^{2}}=1={{\left|{{\lambda }_{ij}}\Psi ({{q}_{1}},{{q}_{2}}...,{{q}_{N}},t)\right|}^{2}}\\&\Rightarrow {{\left|{{\lambda }_{ij}}\right|}^{2}}=1\\&\Rightarrow {{\lambda }_{ij}}=\pm 1\\\end{aligned}}

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MathML (3.038 KB / 474 B) :

\begin{aligned} {| {\hat{p}}_{(i j)} Ψ (q_{1}, q_{2} . . ., q_{N}, t) |}^{2} = {| Ψ (q_{1}, q_{2} . . ., q_{N}, t) |}^{2} = 1 = {| λ_{i j} Ψ (q_{1}, q_{2} . . ., q_{N}, t) |}^{2} \\ \Rightarrow {| λ_{i j} |}^{2} = 1 \\ \Rightarrow λ_{i j} = \pm 1 \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>p</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>i</mi><mi>j</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></msub><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mi>q</mi><mrow data-mjx-texclass="ORD"><mi>N</mi></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msub><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>j</mi></mrow></mrow></msub><mo>=</mo><mo>&#x00B1;</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

$\hat{p}$

$i$

$j$

$Ψ$

$q_{1}$

$q_{2}$

$q_{N}$

$t$

$Ψ$

$q_{1}$

$q_{2}$

$q_{N}$

$t$

$λ_{i j}$

$Ψ$

$q_{1}$

$q_{2}$

$q_{N}$

$t$

$λ_{i j}$

$λ_{i j}$

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