Jump to navigation Jump to search

General

Display information for equation id:math.1719.80 on revision:1719

* Page found: Identische Teilchen: Spin und Statistik (eq math.1719.80)

(force rerendering)

Occurrences on the following pages:

Hash: 031f89aa1a0e36c7b4bb45ecc585f88d

TeX (original user input): 

{{\left| {{\Psi }_{ab}}\left( {{{\bar{r}}}_{1}},{{{\bar{r}}}_{2}} \right) \right|}^{2}}={{\left| \left\langle  {{{\bar{r}}}_{1}}{{{\bar{r}}}_{2}}  |  ab \right\rangle  \right|}^{2}}={{\left| _{1}\left\langle  {{{\bar{r}}}_{1}} \right|{{\left| a \right\rangle }_{1}}_{2}\left\langle  {{{\bar{r}}}_{2}} \right|{{\left| b \right\rangle }_{2}} \right|}^{2}}={{\left| {{\Psi }_{a}}\left( {{{\bar{r}}}_{1}} \right) \right|}^{2}}{{\left| {{\Psi }_{b}}\left( {{{\bar{r}}}_{2}} \right) \right|}^{2}}

TeX (checked): 

{{\left|{{\Psi }_{ab}}\left({{\bar {r}}_{1}},{{\bar {r}}_{2}}\right)\right|}^{2}}={{\left|\left\langle {{\bar {r}}_{1}}{{\bar {r}}_{2}}|ab\right\rangle \right|}^{2}}={{\left|_{1}\left\langle {{\bar {r}}_{1}}\right|{{\left|a\right\rangle }_{1}}_{2}\left\langle {{\bar {r}}_{2}}\right|{{\left|b\right\rangle }_{2}}\right|}^{2}}={{\left|{{\Psi }_{a}}\left({{\bar {r}}_{1}}\right)\right|}^{2}}{{\left|{{\Psi }_{b}}\left({{\bar {r}}_{2}}\right)\right|}^{2}}

LaTeXML (experimental; uses MathML) rendering

MathML (20.093 KB / 2.654 KB) :

| Ψ a ⁢ b ( r ¯ 1 , r ¯ 2 ) | 2 = | ⟨ r ¯ 1 r ¯ 2 | a b ⟩ | 2 = | ⟨ r ¯ 1 | | a ⟩ 1 2 1 ⟨ r ¯ 2 | | b ⟩ 2 | 2 = | Ψ a ( r ¯ 1 ) | 2 | Ψ b ( r ¯ 2 ) | 2 fragments | subscript Ψ 𝑎 𝑏 fragments ( subscript ¯ 𝑟 1 , subscript ¯ 𝑟 2 ) superscript | 2 | fragments ⟨ subscript ¯ 𝑟 1 subscript ¯ 𝑟 2 | a b ⟩ superscript | 2 | subscript subscript subscript fragments ⟨ subscript ¯ 𝑟 1 | | a ⟩ 1 2 1 subscript fragments ⟨ subscript ¯ 𝑟 2 | | b ⟩ 2 superscript | 2 | subscript Ψ 𝑎 fragments ( subscript ¯ 𝑟 1 ) superscript | 2 | subscript Ψ 𝑏 fragments ( subscript ¯ 𝑟 2 ) superscript | 2 {\displaystyle{\displaystyle{{\left|{{\Psi}_{ab}}\left({{{\bar{r}}}_{1}},{{{% \bar{r}}}_{2}}\right)\right|}^{2}}={{\left|\left\langle{{{\bar{r}}}_{1}}{{{% \bar{r}}}_{2}}|ab\right\rangle\right|}^{2}}={{\left|{}_{1}\left\langle{{{\bar{% r}}}_{1}}\right|{{\left|a\right\rangle}_{1}}_{2}\left\langle{{{\bar{r}}}_{2}}% \right|{{\left|b\right\rangle}_{2}}\right|}^{2}}={{\left|{{\Psi}_{a}}\left({{{% \bar{r}}}_{1}}\right)\right|}^{2}}{{\left|{{\Psi}_{b}}\left({{{\bar{r}}}_{2}}% \right)\right|}^{2}}}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{{\left|{{\Psi}_{ab}}\left({{{\bar{r}}}_{1}},{{{%&#10;\bar{r}}}_{2}}\right)\right|}^{2}}={{\left|\left\langle{{{\bar{r}}}_{1}}{{{%&#10;\bar{r}}}_{2}}|ab\right\rangle\right|}^{2}}={{\left|{}_{1}\left\langle{{{\bar{%&#10;r}}}_{1}}\right|{{\left|a\right\rangle}_{1}}_{2}\left\langle{{{\bar{r}}}_{2}}%&#10;\right|{{\left|b\right\rangle}_{2}}\right|}^{2}}={{\left|{{\Psi}_{a}}\left({{{%&#10;\bar{r}}}_{1}}\right)\right|}^{2}}{{\left|{{\Psi}_{b}}\left({{{\bar{r}}}_{2}}%&#10;\right)\right|}^{2}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">|</mo>
      <msub id="p1.1.m1.1.67" xref="p1.1.m1.1.67.cmml">
        <mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Ψ</mi>
        <mrow id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">
          <mi id="p1.1.m1.1.3.1.1" xref="p1.1.m1.1.3.1.1.cmml">a</mi>
          <mo id="p1.1.m1.1.3.1.3" xref="p1.1.m1.1.3.1.3.cmml">⁢</mo>
          <mi id="p1.1.m1.1.3.1.2" xref="p1.1.m1.1.3.1.2.cmml">b</mi>
        </mrow>
      </msub>
      <mrow id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
        <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">(</mo>
        <msub id="p1.1.m1.1.68" xref="p1.1.m1.1.68.cmml">
          <mover accent="true" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">
            <mi id="p1.1.m1.1.5.2" xref="p1.1.m1.1.5.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">,</mo>
        <msub id="p1.1.m1.1.69" xref="p1.1.m1.1.69.cmml">
          <mover accent="true" id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">
            <mi id="p1.1.m1.1.8.2" xref="p1.1.m1.1.8.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">2</mn>
        </msub>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">)</mo>
      </mrow>
      <msup id="p1.1.m1.1.70" xref="p1.1.m1.1.70.cmml">
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">|</mo>
        <mn id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">=</mo>
      <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">|</mo>
      <mrow id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
        <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">⟨</mo>
        <msub id="p1.1.m1.1.71" xref="p1.1.m1.1.71.cmml">
          <mover accent="true" id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">
            <mi id="p1.1.m1.1.16.2" xref="p1.1.m1.1.16.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">1</mn>
        </msub>
        <msub id="p1.1.m1.1.72" xref="p1.1.m1.1.72.cmml">
          <mover accent="true" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
            <mi id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.19.1" xref="p1.1.m1.1.19.1.cmml">2</mn>
        </msub>
        <mo stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">|</mo>
        <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">a</mi>
        <mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">b</mi>
        <mo id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">⟩</mo>
      </mrow>
      <msup id="p1.1.m1.1.73" xref="p1.1.m1.1.73.cmml">
        <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">|</mo>
        <mn id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">=</mo>
      <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">|</mo>
      <mmultiscripts id="p1.1.m1.1.74" xref="p1.1.m1.1.74.cmml">
        <mrow id="p1.1.m1.1.74.2.2.3" xref="p1.1.m1.1.74.2.2.3.cmml">
          <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">⟨</mo>
          <msub id="p1.1.m1.1.74.2.2.2" xref="p1.1.m1.1.74.2.2.2.cmml">
            <mover accent="true" id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">
              <mi id="p1.1.m1.1.30.2" xref="p1.1.m1.1.30.2.cmml">r</mi>
              <mo stretchy="false" id="p1.1.m1.1.30.1" xref="p1.1.m1.1.30.1.cmml">¯</mo>
            </mover>
            <mn id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">1</mn>
          </msub>
          <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">|</mo>
          <mo id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">|</mo>
          <mi id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">a</mi>
          <mo id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">⟩</mo>
        </mrow>
        <mn id="p1.1.m1.1.36.1" xref="p1.1.m1.1.36.1.cmml">1</mn>
        <none id="p1.1.m1.1.74a" xref="p1.1.m1.1.74.cmml"/>
        <mn id="p1.1.m1.1.37.1" xref="p1.1.m1.1.37.1.cmml">2</mn>
        <none id="p1.1.m1.1.74b" xref="p1.1.m1.1.74.cmml"/>
        <mprescripts id="p1.1.m1.1.74c" xref="p1.1.m1.1.74.cmml"/>
        <mn id="p1.1.m1.1.28.1" xref="p1.1.m1.1.28.1.cmml">1</mn>
        <none id="p1.1.m1.1.74d" xref="p1.1.m1.1.74.cmml"/>
      </mmultiscripts>
      <msub id="p1.1.m1.1.75" xref="p1.1.m1.1.75.cmml">
        <mrow id="p1.1.m1.1.75.3" xref="p1.1.m1.1.75.3.cmml">
          <mo id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">⟨</mo>
          <msub id="p1.1.m1.1.75.2" xref="p1.1.m1.1.75.2.cmml">
            <mover accent="true" id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">
              <mi id="p1.1.m1.1.39.2" xref="p1.1.m1.1.39.2.cmml">r</mi>
              <mo stretchy="false" id="p1.1.m1.1.39.1" xref="p1.1.m1.1.39.1.cmml">¯</mo>
            </mover>
            <mn id="p1.1.m1.1.40.1" xref="p1.1.m1.1.40.1.cmml">2</mn>
          </msub>
          <mo id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">|</mo>
          <mo id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">|</mo>
          <mi id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">b</mi>
          <mo id="p1.1.m1.1.44" xref="p1.1.m1.1.44.cmml">⟩</mo>
        </mrow>
        <mn id="p1.1.m1.1.45.1" xref="p1.1.m1.1.45.1.cmml">2</mn>
      </msub>
      <msup id="p1.1.m1.1.76" xref="p1.1.m1.1.76.cmml">
        <mo id="p1.1.m1.1.46" xref="p1.1.m1.1.46.cmml">|</mo>
        <mn id="p1.1.m1.1.47.1" xref="p1.1.m1.1.47.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.48" xref="p1.1.m1.1.48.cmml">=</mo>
      <mo id="p1.1.m1.1.49" xref="p1.1.m1.1.49.cmml">|</mo>
      <msub id="p1.1.m1.1.77" xref="p1.1.m1.1.77.cmml">
        <mi mathvariant="normal" id="p1.1.m1.1.50" xref="p1.1.m1.1.50.cmml">Ψ</mi>
        <mi id="p1.1.m1.1.51.1" xref="p1.1.m1.1.51.1.cmml">a</mi>
      </msub>
      <mrow id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">
        <mo id="p1.1.m1.1.52" xref="p1.1.m1.1.52.cmml">(</mo>
        <msub id="p1.1.m1.1.78" xref="p1.1.m1.1.78.cmml">
          <mover accent="true" id="p1.1.m1.1.53" xref="p1.1.m1.1.53.cmml">
            <mi id="p1.1.m1.1.53.2" xref="p1.1.m1.1.53.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.53.1" xref="p1.1.m1.1.53.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.54.1" xref="p1.1.m1.1.54.1.cmml">1</mn>
        </msub>
        <mo id="p1.1.m1.1.55" xref="p1.1.m1.1.55.cmml">)</mo>
      </mrow>
      <msup id="p1.1.m1.1.79" xref="p1.1.m1.1.79.cmml">
        <mo id="p1.1.m1.1.56" xref="p1.1.m1.1.56.cmml">|</mo>
        <mn id="p1.1.m1.1.57.1" xref="p1.1.m1.1.57.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.58" xref="p1.1.m1.1.58.cmml">|</mo>
      <msub id="p1.1.m1.1.80" xref="p1.1.m1.1.80.cmml">
        <mi mathvariant="normal" id="p1.1.m1.1.59" xref="p1.1.m1.1.59.cmml">Ψ</mi>
        <mi id="p1.1.m1.1.60.1" xref="p1.1.m1.1.60.1.cmml">b</mi>
      </msub>
      <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
        <mo id="p1.1.m1.1.61" xref="p1.1.m1.1.61.cmml">(</mo>
        <msub id="p1.1.m1.1.81" xref="p1.1.m1.1.81.cmml">
          <mover accent="true" id="p1.1.m1.1.62" xref="p1.1.m1.1.62.cmml">
            <mi id="p1.1.m1.1.62.2" xref="p1.1.m1.1.62.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.62.1" xref="p1.1.m1.1.62.1.cmml">¯</mo>
          </mover>
          <mn id="p1.1.m1.1.63.1" xref="p1.1.m1.1.63.1.cmml">2</mn>
        </msub>
        <mo id="p1.1.m1.1.64" xref="p1.1.m1.1.64.cmml">)</mo>
      </mrow>
      <msup id="p1.1.m1.1.82" xref="p1.1.m1.1.82.cmml">
        <mo id="p1.1.m1.1.65" xref="p1.1.m1.1.65.cmml">|</mo>
        <mn id="p1.1.m1.1.66.1" xref="p1.1.m1.1.66.1.cmml">2</mn>
      </msup>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">|</ci>
        <apply id="p1.1.m1.1.67.cmml" xref="p1.1.m1.1.67">
          <csymbol cd="ambiguous" id="p1.1.m1.1.67.1.cmml" xref="p1.1.m1.1.67">subscript</csymbol>
          <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">Ψ</ci>
          <apply id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">
            <times id="p1.1.m1.1.3.1.3.cmml" xref="p1.1.m1.1.3.1.3"/>
            <ci id="p1.1.m1.1.3.1.1.cmml" xref="p1.1.m1.1.3.1.1">𝑎</ci>
            <ci id="p1.1.m1.1.3.1.2.cmml" xref="p1.1.m1.1.3.1.2">𝑏</ci>
          </apply>
        </apply>
        <cerror id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
          <csymbol cd="ambiguous" id="p1.1.m1.1.3a.cmml" xref="p1.1.m1.1.3">fragments</csymbol>
          <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">(</ci>
          <apply id="p1.1.m1.1.68.cmml" xref="p1.1.m1.1.68">
            <csymbol cd="ambiguous" id="p1.1.m1.1.68.1.cmml" xref="p1.1.m1.1.68">subscript</csymbol>
            <apply id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">
              <ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">¯</ci>
              <ci id="p1.1.m1.1.5.2.cmml" xref="p1.1.m1.1.5.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">1</cn>
          </apply>
          <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">,</ci>
          <apply id="p1.1.m1.1.69.cmml" xref="p1.1.m1.1.69">
            <csymbol cd="ambiguous" id="p1.1.m1.1.69.1.cmml" xref="p1.1.m1.1.69">subscript</csymbol>
            <apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">
              <ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">¯</ci>
              <ci id="p1.1.m1.1.8.2.cmml" xref="p1.1.m1.1.8.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">)</ci>
        </cerror>
        <apply id="p1.1.m1.1.70.cmml" xref="p1.1.m1.1.70">
          <csymbol cd="ambiguous" id="p1.1.m1.1.70.1.cmml" xref="p1.1.m1.1.70">superscript</csymbol>
          <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">|</ci>
          <cn type="integer" id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">2</cn>
        </apply>
        <eq id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
        <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">|</ci>
        <cerror id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
          <csymbol cd="ambiguous" id="p1.1.m1.1.6a.cmml" xref="p1.1.m1.1.6">fragments</csymbol>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">⟨</ci>
          <apply id="p1.1.m1.1.71.cmml" xref="p1.1.m1.1.71">
            <csymbol cd="ambiguous" id="p1.1.m1.1.71.1.cmml" xref="p1.1.m1.1.71">subscript</csymbol>
            <apply id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">
              <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">¯</ci>
              <ci id="p1.1.m1.1.16.2.cmml" xref="p1.1.m1.1.16.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">1</cn>
          </apply>
          <apply id="p1.1.m1.1.72.cmml" xref="p1.1.m1.1.72">
            <csymbol cd="ambiguous" id="p1.1.m1.1.72.1.cmml" xref="p1.1.m1.1.72">subscript</csymbol>
            <apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">
              <ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">¯</ci>
              <ci id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">|</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">a</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">b</csymbol>
          <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">⟩</ci>
        </cerror>
        <apply id="p1.1.m1.1.73.cmml" xref="p1.1.m1.1.73">
          <csymbol cd="ambiguous" id="p1.1.m1.1.73.1.cmml" xref="p1.1.m1.1.73">superscript</csymbol>
          <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">|</ci>
          <cn type="integer" id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">2</cn>
        </apply>
        <eq id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26"/>
        <ci id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">|</ci>
        <apply id="p1.1.m1.1.74.cmml" xref="p1.1.m1.1.74">
          <csymbol cd="ambiguous" id="p1.1.m1.1.74.1.cmml" xref="p1.1.m1.1.74">subscript</csymbol>
          <apply id="p1.1.m1.1.74.2.cmml" xref="p1.1.m1.1.74">
            <csymbol cd="ambiguous" id="p1.1.m1.1.74.2.1.cmml" xref="p1.1.m1.1.74">subscript</csymbol>
            <apply id="p1.1.m1.1.74.2.2.cmml" xref="p1.1.m1.1.74">
              <csymbol cd="ambiguous" id="p1.1.m1.1.74.2.2.1.cmml" xref="p1.1.m1.1.74">subscript</csymbol>
              <cerror id="p1.1.m1.1.74.2.2.3.cmml" xref="p1.1.m1.1.74.2.2.3">
                <csymbol cd="ambiguous" id="p1.1.m1.1.74.2.2.3a.cmml" xref="p1.1.m1.1.74.2.2.3">fragments</csymbol>
                <ci id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">⟨</ci>
                <apply id="p1.1.m1.1.74.2.2.2.cmml" xref="p1.1.m1.1.74.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.74.2.2.2.1.cmml" xref="p1.1.m1.1.74.2.2.2">subscript</csymbol>
                  <apply id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">
                    <ci id="p1.1.m1.1.30.1.cmml" xref="p1.1.m1.1.30.1">¯</ci>
                    <ci id="p1.1.m1.1.30.2.cmml" xref="p1.1.m1.1.30.2">𝑟</ci>
                  </apply>
                  <cn type="integer" id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">1</cn>
                </apply>
                <ci id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">|</ci>
                <ci id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">|</ci>
                <csymbol cd="unknown" id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">a</csymbol>
                <ci id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">⟩</ci>
              </cerror>
              <cn type="integer" id="p1.1.m1.1.36.1.cmml" xref="p1.1.m1.1.36.1">1</cn>
            </apply>
            <cn type="integer" id="p1.1.m1.1.37.1.cmml" xref="p1.1.m1.1.37.1">2</cn>
          </apply>
          <cn type="integer" id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28.1">1</cn>
        </apply>
        <apply id="p1.1.m1.1.75.cmml" xref="p1.1.m1.1.75">
          <csymbol cd="ambiguous" id="p1.1.m1.1.75.1.cmml" xref="p1.1.m1.1.75">subscript</csymbol>
          <cerror id="p1.1.m1.1.75.3.cmml" xref="p1.1.m1.1.75.3">
            <csymbol cd="ambiguous" id="p1.1.m1.1.75.3a.cmml" xref="p1.1.m1.1.75.3">fragments</csymbol>
            <ci id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38">⟨</ci>
            <apply id="p1.1.m1.1.75.2.cmml" xref="p1.1.m1.1.75.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.75.2.1.cmml" xref="p1.1.m1.1.75.2">subscript</csymbol>
              <apply id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">
                <ci id="p1.1.m1.1.39.1.cmml" xref="p1.1.m1.1.39.1">¯</ci>
                <ci id="p1.1.m1.1.39.2.cmml" xref="p1.1.m1.1.39.2">𝑟</ci>
              </apply>
              <cn type="integer" id="p1.1.m1.1.40.1.cmml" xref="p1.1.m1.1.40.1">2</cn>
            </apply>
            <ci id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">|</ci>
            <ci id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">|</ci>
            <csymbol cd="unknown" id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">b</csymbol>
            <ci id="p1.1.m1.1.44.cmml" xref="p1.1.m1.1.44">⟩</ci>
          </cerror>
          <cn type="integer" id="p1.1.m1.1.45.1.cmml" xref="p1.1.m1.1.45.1">2</cn>
        </apply>
        <apply id="p1.1.m1.1.76.cmml" xref="p1.1.m1.1.76">
          <csymbol cd="ambiguous" id="p1.1.m1.1.76.1.cmml" xref="p1.1.m1.1.76">superscript</csymbol>
          <ci id="p1.1.m1.1.46.cmml" xref="p1.1.m1.1.46">|</ci>
          <cn type="integer" id="p1.1.m1.1.47.1.cmml" xref="p1.1.m1.1.47.1">2</cn>
        </apply>
        <eq id="p1.1.m1.1.48.cmml" xref="p1.1.m1.1.48"/>
        <ci id="p1.1.m1.1.49.cmml" xref="p1.1.m1.1.49">|</ci>
        <apply id="p1.1.m1.1.77.cmml" xref="p1.1.m1.1.77">
          <csymbol cd="ambiguous" id="p1.1.m1.1.77.1.cmml" xref="p1.1.m1.1.77">subscript</csymbol>
          <ci id="p1.1.m1.1.50.cmml" xref="p1.1.m1.1.50">Ψ</ci>
          <ci id="p1.1.m1.1.51.1.cmml" xref="p1.1.m1.1.51.1">𝑎</ci>
        </apply>
        <cerror id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">
          <csymbol cd="ambiguous" id="p1.1.m1.1.9a.cmml" xref="p1.1.m1.1.9">fragments</csymbol>
          <ci id="p1.1.m1.1.52.cmml" xref="p1.1.m1.1.52">(</ci>
          <apply id="p1.1.m1.1.78.cmml" xref="p1.1.m1.1.78">
            <csymbol cd="ambiguous" id="p1.1.m1.1.78.1.cmml" xref="p1.1.m1.1.78">subscript</csymbol>
            <apply id="p1.1.m1.1.53.cmml" xref="p1.1.m1.1.53">
              <ci id="p1.1.m1.1.53.1.cmml" xref="p1.1.m1.1.53.1">¯</ci>
              <ci id="p1.1.m1.1.53.2.cmml" xref="p1.1.m1.1.53.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.54.1.cmml" xref="p1.1.m1.1.54.1">1</cn>
          </apply>
          <ci id="p1.1.m1.1.55.cmml" xref="p1.1.m1.1.55">)</ci>
        </cerror>
        <apply id="p1.1.m1.1.79.cmml" xref="p1.1.m1.1.79">
          <csymbol cd="ambiguous" id="p1.1.m1.1.79.1.cmml" xref="p1.1.m1.1.79">superscript</csymbol>
          <ci id="p1.1.m1.1.56.cmml" xref="p1.1.m1.1.56">|</ci>
          <cn type="integer" id="p1.1.m1.1.57.1.cmml" xref="p1.1.m1.1.57.1">2</cn>
        </apply>
        <ci id="p1.1.m1.1.58.cmml" xref="p1.1.m1.1.58">|</ci>
        <apply id="p1.1.m1.1.80.cmml" xref="p1.1.m1.1.80">
          <csymbol cd="ambiguous" id="p1.1.m1.1.80.1.cmml" xref="p1.1.m1.1.80">subscript</csymbol>
          <ci id="p1.1.m1.1.59.cmml" xref="p1.1.m1.1.59">Ψ</ci>
          <ci id="p1.1.m1.1.60.1.cmml" xref="p1.1.m1.1.60.1">𝑏</ci>
        </apply>
        <cerror id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
          <csymbol cd="ambiguous" id="p1.1.m1.1.12a.cmml" xref="p1.1.m1.1.12">fragments</csymbol>
          <ci id="p1.1.m1.1.61.cmml" xref="p1.1.m1.1.61">(</ci>
          <apply id="p1.1.m1.1.81.cmml" xref="p1.1.m1.1.81">
            <csymbol cd="ambiguous" id="p1.1.m1.1.81.1.cmml" xref="p1.1.m1.1.81">subscript</csymbol>
            <apply id="p1.1.m1.1.62.cmml" xref="p1.1.m1.1.62">
              <ci id="p1.1.m1.1.62.1.cmml" xref="p1.1.m1.1.62.1">¯</ci>
              <ci id="p1.1.m1.1.62.2.cmml" xref="p1.1.m1.1.62.2">𝑟</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.63.1.cmml" xref="p1.1.m1.1.63.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.64.cmml" xref="p1.1.m1.1.64">)</ci>
        </cerror>
        <apply id="p1.1.m1.1.82.cmml" xref="p1.1.m1.1.82">
          <csymbol cd="ambiguous" id="p1.1.m1.1.82.1.cmml" xref="p1.1.m1.1.82">superscript</csymbol>
          <ci id="p1.1.m1.1.65.cmml" xref="p1.1.m1.1.65">|</ci>
          <cn type="integer" id="p1.1.m1.1.66.1.cmml" xref="p1.1.m1.1.66.1">2</cn>
        </apply>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle{{\left|{{\Psi}_{ab}}\left({{{\bar{r}}}_{1}},{{{%
\bar{r}}}_{2}}\right)\right|}^{2}}={{\left|\left\langle{{{\bar{r}}}_{1}}{{{%
\bar{r}}}_{2}}|ab\right\rangle\right|}^{2}}={{\left|{}_{1}\left\langle{{{\bar{%
r}}}_{1}}\right|{{\left|a\right\rangle}_{1}}_{2}\left\langle{{{\bar{r}}}_{2}}%
\right|{{\left|b\right\rangle}_{2}}\right|}^{2}}={{\left|{{\Psi}_{a}}\left({{{%
\bar{r}}}_{1}}\right)\right|}^{2}}{{\left|{{\Psi}_{b}}\left({{{\bar{r}}}_{2}}%
\right)\right|}^{2}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (3.881 KB / 415 B) :

|Ψab(r¯1,r¯2)|2=|⟨r¯1r¯2|ab⟩|2=|1⟨r¯1||a⟩12⟨r¯2||b⟩2|2=|Ψa(r¯1)|2|Ψb(r¯2)|2
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>a</mi><mi>b</mi></mrow></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>|</mo><mi>a</mi><mi>b</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><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><msub><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>a</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><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><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>b</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Identische Teilchen: Spin und Statistik page

Identifiers

  • Ψab
  • r¯1
  • r¯2
  • r¯1
  • r¯2
  • a
  • b
  • r¯1
  • a12
  • r¯2
  • b2
  • Ψa
  • r¯1
  • Ψb
  • r¯2

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"