– PhysikWiki

General

Display information for equation id:math.1632.61 on revision:1632

* Page found: Eigenwerte und Eigenzustände von hermiteschen Operatoren (eq math.1632.61)

Occurrences on the following pages:

Eigenwerte und Eigenzustände von hermiteschen Operatoren Eq: math.1632.61

Hash: 6f9913f2c735d813f84c4d1eb3c96b30

TeX (original user input):

\left\langle  \Phi \acute{\ }  |  \Psi \acute{\ } \right\rangle :=\left\langle  \Phi  \right|{{U}^{+}}U\left| \Psi  \right\rangle =\left\langle  \Phi   |  \Psi  \right\rangle

TeX (checked):

\left\langle \Phi {\acute {\ }}|\Psi {\acute {\ }}\right\rangle :=\left\langle \Phi \right|{{U}^{+}}U\left|\Psi \right\rangle =\left\langle \Phi |\Psi \right\rangle

LaTeXML (experimentell; verwendet MathML) rendering

MathML (6.4 KB / 1.137 KB) :

{\displaystyle{\displaystyle\left\langle\Phi\acute{\ }|\Psi\acute{\ }\right% \rangle:=\left\langle\Phi\right|{{U}^{+}}U\left|\Psi\right\rangle=\left\langle% \Phi|\Psi\right\rangle}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left\langle\Phi\acute{\ }|\Psi\acute{\ }\right%&#10;\rangle:=\left\langle\Phi\right|{{U}^{+}}U\left|\Psi\right\rangle=\left\langle%&#10;\Phi|\Psi\right\rangle}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">
      <mrow id="p1.1.m1.1.25.2" xref="p1.1.m1.1.25.2.1.cmml">
        <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.25.2.1.1.cmml">⟨</mo>
        <mrow id="p1.1.m1.1.25.2.2" xref="p1.1.m1.1.25.2.2.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Φ</mi>
          <mo id="p1.1.m1.1.25.2.2.1" xref="p1.1.m1.1.25.2.2.1.cmml">⁢</mo>
          <mover accent="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
            <mi id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml"/>
            <mo id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">´</mo>
          </mover>
        </mrow>
        <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.25.2.1.1.cmml">|</mo>
        <mrow id="p1.1.m1.1.25.2.3" xref="p1.1.m1.1.25.2.3.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">Ψ</mi>
          <mo id="p1.1.m1.1.25.2.3.1" xref="p1.1.m1.1.25.2.3.1.cmml">⁢</mo>
          <mover accent="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
            <mi id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml"/>
            <mo id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">´</mo>
          </mover>
        </mrow>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.25.2.1.1.cmml">⟩</mo>
      </mrow>
      <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">:=</mo>
      <mrow id="p1.1.m1.1.25.3" xref="p1.1.m1.1.25.3.1.cmml">
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.25.3.1.1.cmml">⟨</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">Φ</mi>
        <mo fence="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.25.3.1.1.cmml">|</mo>
        <mrow id="p1.1.m1.1.25.3.2" xref="p1.1.m1.1.25.3.2.cmml">
          <msup id="p1.1.m1.1.25.3.2.2" xref="p1.1.m1.1.25.3.2.2.cmml">
            <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">U</mi>
            <mo id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">+</mo>
          </msup>
          <mo id="p1.1.m1.1.25.3.2.1" xref="p1.1.m1.1.25.3.2.1.cmml">⁢</mo>
          <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">U</mi>
        </mrow>
        <mo fence="true" id="p1.1.m1.1.16" xref="p1.1.m1.1.25.3.1.1.cmml">|</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">Ψ</mi>
        <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.25.3.1.1.cmml">⟩</mo>
      </mrow>
      <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">=</mo>
      <mrow id="p1.1.m1.1.25.4" xref="p1.1.m1.1.25.4.1.cmml">
        <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.25.4.1.1.cmml">⟨</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">Φ</mi>
        <mo stretchy="false" id="p1.1.m1.1.22" xref="p1.1.m1.1.25.4.1.1.cmml">|</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">Ψ</mi>
        <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.25.4.1.1.cmml">⟩</mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">
        <and id="p1.1.m1.1.25a.cmml" xref="p1.1.m1.1.25"/>
        <apply id="p1.1.m1.1.25b.cmml" xref="p1.1.m1.1.25">
          <csymbol cd="latexml" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">assign</csymbol>
          <apply id="p1.1.m1.1.25.2.1.cmml" xref="p1.1.m1.1.25.2">
            <csymbol cd="latexml" id="p1.1.m1.1.25.2.1.1.cmml" xref="p1.1.m1.1.1">inner-product</csymbol>
            <apply id="p1.1.m1.1.25.2.2.cmml" xref="p1.1.m1.1.25.2.2">
              <times id="p1.1.m1.1.25.2.2.1.cmml" xref="p1.1.m1.1.25.2.2.1"/>
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">Φ</ci>
              <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
                <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">´</ci>
                <csymbol cd="latexml" id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">absent</csymbol>
              </apply>
            </apply>
            <apply id="p1.1.m1.1.25.2.3.cmml" xref="p1.1.m1.1.25.2.3">
              <times id="p1.1.m1.1.25.2.3.1.cmml" xref="p1.1.m1.1.25.2.3.1"/>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">Ψ</ci>
              <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
                <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">´</ci>
                <csymbol cd="latexml" id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">absent</csymbol>
              </apply>
            </apply>
          </apply>
          <apply id="p1.1.m1.1.25.3.1.cmml" xref="p1.1.m1.1.25.3">
            <csymbol cd="latexml" id="p1.1.m1.1.25.3.1.1.cmml" xref="p1.1.m1.1.10">quantum-operator-product</csymbol>
            <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">Φ</ci>
            <apply id="p1.1.m1.1.25.3.2.cmml" xref="p1.1.m1.1.25.3.2">
              <times id="p1.1.m1.1.25.3.2.1.cmml" xref="p1.1.m1.1.25.3.2.1"/>
              <apply id="p1.1.m1.1.25.3.2.2.cmml" xref="p1.1.m1.1.25.3.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.25.3.2.2.1.cmml" xref="p1.1.m1.1.25.3.2.2">superscript</csymbol>
                <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝑈</ci>
                <plus id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1"/>
              </apply>
              <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝑈</ci>
            </apply>
            <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">Ψ</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.25c.cmml" xref="p1.1.m1.1.25">
          <eq id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
          <share href="#p1.1.m1.1.25.3.cmml" id="p1.1.m1.1.25d.cmml" xref="p1.1.m1.1.25"/>
          <apply id="p1.1.m1.1.25.4.1.cmml" xref="p1.1.m1.1.25.4">
            <csymbol cd="latexml" id="p1.1.m1.1.25.4.1.1.cmml" xref="p1.1.m1.1.20">inner-product</csymbol>
            <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">Φ</ci>
            <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">Ψ</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left\langle\Phi\acute{\ }|\Psi\acute{\ }\right%
\rangle:=\left\langle\Phi\right|{{U}^{+}}U\left|\Psi\right\rangle=\left\langle%
\Phi|\Psi\right\rangle}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (1.284 KB / 320 B) :

⟨ Φ \overset{´}{} | Ψ \overset{´}{} ⟩ : = ⟨ Φ | U^{+} U | Ψ ⟩ = ⟨ Φ | Ψ ⟩

<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="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>|</mo><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mi>:</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A6;</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mi>U</mi><mrow data-mjx-texclass="ORD"><mo>+</mo></mrow></msup><mi>U</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</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><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$Φ$

$\overset{´}{}$

$Ψ$

$\overset{´}{}$

$Φ$

$U$

$U$

$Ψ$

$Φ$

$Ψ$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche