Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2710.60 on revision:2710

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2710.60)

(force rerendering)

Occurrences on the following pages:

Hash: c6d21a9ebd1d1e749c2071dd6610cdf2

TeX (original user input):

{{\left\| \Phi  \right\|}^{2}}=\left\langle  \Phi  | \Phi  \right\rangle =\left\langle \Phi |\underline{1}|\Phi  \right\rangle =\sum\limits_{n}{\left\langle  \Phi  | n \right\rangle }\left\langle  n | \Phi  \right\rangle ={{\sum\limits_{n}{\left| \left\langle  n | \Phi  \right\rangle  \right|}}^{2}}

TeX (checked):

{{\left\|\Phi \right\|}^{2}}=\left\langle \Phi |\Phi \right\rangle =\left\langle \Phi |{\underline {1}}|\Phi \right\rangle =\sum \limits _{n}{\left\langle \Phi |n\right\rangle }\left\langle n|\Phi \right\rangle ={{\sum \limits _{n}{\left|\left\langle n|\Phi \right\rangle \right|}}^{2}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (10.675 KB / 1.639 KB) :

Φ 2 = Φ | Φ = Φ | 1 ¯ | Φ = n Φ | n n | Φ = n | n | Φ | 2 superscript norm Φ 2 inner-product Φ Φ quantum-operator-product Φ ¯ 1 Φ subscript 𝑛 inner-product Φ 𝑛 inner-product 𝑛 Φ subscript 𝑛 superscript inner-product 𝑛 Φ 2 {\displaystyle{\displaystyle{{\left\|\Phi\right\|}^{2}}=\left\langle\Phi|\Phi% \right\rangle=\left\langle\Phi|\underline{1}|\Phi\right\rangle=\sum\limits_{n}% {\left\langle\Phi|n\right\rangle}\left\langle n|\Phi\right\rangle={{\sum% \limits_{n}{\left|\left\langle n|\Phi\right\rangle\right|}}^{2}}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{{\left\|\Phi\right\|}^{2}}=\left\langle\Phi|\Phi%&#10;\right\rangle=\left\langle\Phi|\underline{1}|\Phi\right\rangle=\sum\limits_{n}%&#10;{\left\langle\Phi|n\right\rangle}\left\langle n|\Phi\right\rangle={{\sum%&#10;\limits_{n}{\left|\left\langle n|\Phi\right\rangle\right|}}^{2}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">
      <msup id="p1.1.m1.1.43.2" xref="p1.1.m1.1.43.2.cmml">
        <mrow id="p1.1.m1.1.43.2.2" xref="p1.1.m1.1.43.2.2.1.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.43.2.2.1.1.cmml"></mo>
          <mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Φ</mi>
          <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.43.2.2.1.1.cmml"></mo>
        </mrow>
        <mn id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
      <mrow id="p1.1.m1.1.43.3" xref="p1.1.m1.1.43.3.1.cmml">
        <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.43.3.1.1.cmml"></mo>
        <mi mathvariant="normal" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">Φ</mi>
        <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.43.3.1.1.cmml">|</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">Φ</mi>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.43.3.1.1.cmml"></mo>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
      <mrow id="p1.1.m1.1.43.4" xref="p1.1.m1.1.43.4.1.cmml">
        <mo id="p1.1.m1.1.12" xref="p1.1.m1.1.43.4.1.1.cmml"></mo>
        <mi mathvariant="normal" id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">Φ</mi>
        <mo fence="true" stretchy="false" id="p1.1.m1.1.14" xref="p1.1.m1.1.43.4.1.1.cmml">|</mo>
        <munder accentunder="true" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">
          <mn id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">1</mn>
          <mo id="p1.1.m1.1.15.1" xref="p1.1.m1.1.15.1.cmml">¯</mo>
        </munder>
        <mo fence="true" stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.43.4.1.1.cmml">|</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">Φ</mi>
        <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.43.4.1.1.cmml"></mo>
      </mrow>
      <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">=</mo>
      <mrow id="p1.1.m1.1.43.5" xref="p1.1.m1.1.43.5.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.43.5.1" xref="p1.1.m1.1.43.5.1.cmml">
          <munder id="p1.1.m1.1.43.5.1a" xref="p1.1.m1.1.43.5.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml"></mo>
            <mi id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">n</mi>
          </munder>
        </mstyle>
        <mrow id="p1.1.m1.1.43.5.2" xref="p1.1.m1.1.43.5.2.cmml">
          <mrow id="p1.1.m1.1.43.5.2.2" xref="p1.1.m1.1.43.5.2.2.1.cmml">
            <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.43.5.2.2.1.1.cmml"></mo>
            <mi mathvariant="normal" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">Φ</mi>
            <mo stretchy="false" id="p1.1.m1.1.24" xref="p1.1.m1.1.43.5.2.2.1.1.cmml">|</mo>
            <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">n</mi>
            <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.43.5.2.2.1.1.cmml"></mo>
          </mrow>
          <mo id="p1.1.m1.1.43.5.2.1" xref="p1.1.m1.1.43.5.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.43.5.2.3" xref="p1.1.m1.1.43.5.2.3.1.cmml">
            <mo id="p1.1.m1.1.27" xref="p1.1.m1.1.43.5.2.3.1.1.cmml"></mo>
            <mi id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">n</mi>
            <mo stretchy="false" id="p1.1.m1.1.29" xref="p1.1.m1.1.43.5.2.3.1.1.cmml">|</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">Φ</mi>
            <mo id="p1.1.m1.1.31" xref="p1.1.m1.1.43.5.2.3.1.1.cmml"></mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">=</mo>
      <mrow id="p1.1.m1.1.43.6" xref="p1.1.m1.1.43.6.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.43.6.1" xref="p1.1.m1.1.43.6.1.cmml">
          <munder id="p1.1.m1.1.43.6.1a" xref="p1.1.m1.1.43.6.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml"></mo>
            <mi id="p1.1.m1.1.34.1" xref="p1.1.m1.1.34.1.cmml">n</mi>
          </munder>
        </mstyle>
        <msup id="p1.1.m1.1.43.6.2" xref="p1.1.m1.1.43.6.2.cmml">
          <mrow id="p1.1.m1.1.43.6.2.2" xref="p1.1.m1.1.43.6.2.2.1.cmml">
            <mo id="p1.1.m1.1.35" xref="p1.1.m1.1.43.6.2.2.1.1.cmml">|</mo>
            <mrow id="p1.1.m1.1.43.6.2.2.2" xref="p1.1.m1.1.43.6.2.2.2.1.cmml">
              <mo id="p1.1.m1.1.36" xref="p1.1.m1.1.43.6.2.2.2.1.1.cmml"></mo>
              <mi id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">n</mi>
              <mo stretchy="false" id="p1.1.m1.1.38" xref="p1.1.m1.1.43.6.2.2.2.1.1.cmml">|</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">Φ</mi>
              <mo id="p1.1.m1.1.40" xref="p1.1.m1.1.43.6.2.2.2.1.1.cmml"></mo>
            </mrow>
            <mo id="p1.1.m1.1.41" xref="p1.1.m1.1.43.6.2.2.1.1.cmml">|</mo>
          </mrow>
          <mn id="p1.1.m1.1.42.1" xref="p1.1.m1.1.42.1.cmml">2</mn>
        </msup>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">
        <and id="p1.1.m1.1.43a.cmml" xref="p1.1.m1.1.43"/>
        <apply id="p1.1.m1.1.43b.cmml" xref="p1.1.m1.1.43">
          <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <apply id="p1.1.m1.1.43.2.cmml" xref="p1.1.m1.1.43.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.43.2.1.cmml" xref="p1.1.m1.1.43.2">superscript</csymbol>
            <apply id="p1.1.m1.1.43.2.2.1.cmml" xref="p1.1.m1.1.43.2.2">
              <csymbol cd="latexml" id="p1.1.m1.1.43.2.2.1.1.cmml" xref="p1.1.m1.1.1">norm</csymbol>
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">Φ</ci>
            </apply>
            <cn type="integer" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">2</cn>
          </apply>
          <apply id="p1.1.m1.1.43.3.1.cmml" xref="p1.1.m1.1.43.3">
            <csymbol cd="latexml" id="p1.1.m1.1.43.3.1.1.cmml" xref="p1.1.m1.1.6">inner-product</csymbol>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">Φ</ci>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">Φ</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.43c.cmml" xref="p1.1.m1.1.43">
          <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
          <share href="#p1.1.m1.1.43.3.cmml" id="p1.1.m1.1.43d.cmml" xref="p1.1.m1.1.43"/>
          <apply id="p1.1.m1.1.43.4.1.cmml" xref="p1.1.m1.1.43.4">
            <csymbol cd="latexml" id="p1.1.m1.1.43.4.1.1.cmml" xref="p1.1.m1.1.12">quantum-operator-product</csymbol>
            <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">Φ</ci>
            <apply id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">
              <ci id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15.1">¯</ci>
              <cn type="integer" id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">1</cn>
            </apply>
            <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">Φ</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.43e.cmml" xref="p1.1.m1.1.43">
          <eq id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
          <share href="#p1.1.m1.1.43.4.cmml" id="p1.1.m1.1.43f.cmml" xref="p1.1.m1.1.43"/>
          <apply id="p1.1.m1.1.43.5.cmml" xref="p1.1.m1.1.43.5">
            <apply id="p1.1.m1.1.43.5.1.cmml" xref="p1.1.m1.1.43.5.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.43.5.1.1.cmml" xref="p1.1.m1.1.43.5.1">subscript</csymbol>
              <sum id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"/>
              <ci id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">𝑛</ci>
            </apply>
            <apply id="p1.1.m1.1.43.5.2.cmml" xref="p1.1.m1.1.43.5.2">
              <times id="p1.1.m1.1.43.5.2.1.cmml" xref="p1.1.m1.1.43.5.2.1"/>
              <apply id="p1.1.m1.1.43.5.2.2.1.cmml" xref="p1.1.m1.1.43.5.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.43.5.2.2.1.1.cmml" xref="p1.1.m1.1.22">inner-product</csymbol>
                <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">Φ</ci>
                <ci id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">𝑛</ci>
              </apply>
              <apply id="p1.1.m1.1.43.5.2.3.1.cmml" xref="p1.1.m1.1.43.5.2.3">
                <csymbol cd="latexml" id="p1.1.m1.1.43.5.2.3.1.1.cmml" xref="p1.1.m1.1.27">inner-product</csymbol>
                <ci id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28">𝑛</ci>
                <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">Φ</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.43g.cmml" xref="p1.1.m1.1.43">
          <eq id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32"/>
          <share href="#p1.1.m1.1.43.5.cmml" id="p1.1.m1.1.43h.cmml" xref="p1.1.m1.1.43"/>
          <apply id="p1.1.m1.1.43.6.cmml" xref="p1.1.m1.1.43.6">
            <apply id="p1.1.m1.1.43.6.1.cmml" xref="p1.1.m1.1.43.6.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.43.6.1.1.cmml" xref="p1.1.m1.1.43.6.1">subscript</csymbol>
              <sum id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33"/>
              <ci id="p1.1.m1.1.34.1.cmml" xref="p1.1.m1.1.34.1">𝑛</ci>
            </apply>
            <apply id="p1.1.m1.1.43.6.2.cmml" xref="p1.1.m1.1.43.6.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.43.6.2.1.cmml" xref="p1.1.m1.1.43.6.2">superscript</csymbol>
              <apply id="p1.1.m1.1.43.6.2.2.1.cmml" xref="p1.1.m1.1.43.6.2.2">
                <abs id="p1.1.m1.1.43.6.2.2.1.1.cmml" xref="p1.1.m1.1.35"/>
                <apply id="p1.1.m1.1.43.6.2.2.2.1.cmml" xref="p1.1.m1.1.43.6.2.2.2">
                  <csymbol cd="latexml" id="p1.1.m1.1.43.6.2.2.2.1.1.cmml" xref="p1.1.m1.1.36">inner-product</csymbol>
                  <ci id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">𝑛</ci>
                  <ci id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39">Φ</ci>
                </apply>
              </apply>
              <cn type="integer" id="p1.1.m1.1.42.1.cmml" xref="p1.1.m1.1.42.1">2</cn>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{{\left\|\Phi\right\|}^{2}}=\left\langle\Phi|\Phi%
\right\rangle=\left\langle\Phi|\underline{1}|\Phi\right\rangle=\sum\limits_{n}%
{\left\langle\Phi|n\right\rangle}\left\langle n|\Phi\right\rangle={{\sum%
\limits_{n}{\left|\left\langle n|\Phi\right\rangle\right|}}^{2}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimentell; keine Bilder) rendering

MathML (1.863 KB / 345 B) :

Φ2=Φ|Φ=Φ|1_|Φ=nΦ|nn|Φ=n|n|Φ|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">&#x2016;</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">&#x2016;</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A6;</mi><mo>|</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A6;</mi><mo>|</mo><mrow data-mjx-texclass="ORD"><munder><mn>1</mn><mo>_</mo></munder></mrow><mo>|</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A6;</mi><mo>|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi>n</mi><mo>|</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><msup><mrow data-mjx-texclass="ORD"><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi>n</mi><mo>|</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></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 Formaler Aufbau der Quantenmechanik page

Identifiers

  • Φ
  • Φ
  • Φ
  • Φ
  • 1_
  • Φ
  • n
  • Φ
  • n
  • n
  • Φ
  • n
  • n
  • Φ

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results