Jump to navigation Jump to search

General

Display information for equation id:math.1623.41 on revision:1623

* Page found: Operatoren im Hilbertraum (eq math.1623.41)

(force rerendering)

Occurrences on the following pages:

Hash: cc3ca84b6214038003aff34a6e364961

TeX (original user input): 

\left( {{\Psi }_{1}},\hat{F}{{\Psi }_{2}} \right)=\left( \hat{F}{{\Psi }_{1}},{{\Psi }_{2}} \right)\quad \forall {{\Psi }_{1}},{{\Psi }_{2}}\in H

TeX (checked): 

\left({{\Psi }_{1}},{\hat {F}}{{\Psi }_{2}}\right)=\left({\hat {F}}{{\Psi }_{1}},{{\Psi }_{2}}\right)\quad \forall {{\Psi }_{1}},{{\Psi }_{2}}\in H

LaTeXML (experimental; uses MathML) rendering

MathML (8.443 KB / 1.385 KB) :

( Ψ 1 , F ^ ⁢ Ψ 2 ) = ( F ^ ⁢ Ψ 1 , Ψ 2 )   ∀ Ψ 1 , Ψ 2 ∈ H formulae-sequence subscript Ψ 1 ^ 𝐹 subscript Ψ 2 ^ 𝐹 subscript Ψ 1 subscript Ψ 2 for-all subscript Ψ 1 subscript Ψ 2 𝐻 {\displaystyle{\displaystyle\left({{\Psi}_{1}},\hat{F}{{\Psi}_{2}}\right)=% \left(\hat{F}{{\Psi}_{1}},{{\Psi}_{2}}\right)\quad\forall{{\Psi}_{1}},{{\Psi}_% {2}}\in H}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left({{\Psi}_{1}},\hat{F}{{\Psi}_{2}}\right)=%&#10;\left(\hat{F}{{\Psi}_{1}},{{\Psi}_{2}}\right)\quad\forall{{\Psi}_{1}},{{\Psi}_%&#10;{2}}\in H}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.28" xref="p1.1.m1.1.28.1.cmml">
      <mrow id="p1.1.m1.1.28.2" xref="p1.1.m1.1.28.2.cmml">
        <mrow id="p1.1.m1.1.28.2.1" xref="p1.1.m1.1.28.2.1.1.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.28.2.1.1.cmml">(</mo>
          <msub id="p1.1.m1.1.28.2.1.2" xref="p1.1.m1.1.28.2.1.2.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">Ψ</mi>
            <mn id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">1</mn>
          </msub>
          <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.28.2.1.1.cmml">,</mo>
          <mrow id="p1.1.m1.1.28.2.1.3" xref="p1.1.m1.1.28.2.1.3.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">F</mi>
              <mo stretchy="false" id="p1.1.m1.1.5.1" xref="p1.1.m1.1.5.1.cmml">^</mo>
            </mover>
            <mo id="p1.1.m1.1.28.2.1.3.1" xref="p1.1.m1.1.28.2.1.3.1.cmml">⁢</mo>
            <msub id="p1.1.m1.1.28.2.1.3.2" xref="p1.1.m1.1.28.2.1.3.2.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">Ψ</mi>
              <mn id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">2</mn>
            </msub>
          </mrow>
          <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.28.2.1.1.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">=</mo>
        <mrow id="p1.1.m1.1.28.2.2" xref="p1.1.m1.1.28.2.2.1.cmml">
          <mrow id="p1.1.m1.1.28.2.2.2" xref="p1.1.m1.1.28.2.2.2.1.cmml">
            <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.28.2.2.2.1.cmml">(</mo>
            <mrow id="p1.1.m1.1.28.2.2.2.2" xref="p1.1.m1.1.28.2.2.2.2.cmml">
              <mover accent="true" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">
                <mi id="p1.1.m1.1.11.2" xref="p1.1.m1.1.11.2.cmml">F</mi>
                <mo stretchy="false" id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml">^</mo>
              </mover>
              <mo id="p1.1.m1.1.28.2.2.2.2.1" xref="p1.1.m1.1.28.2.2.2.2.1.cmml">⁢</mo>
              <msub id="p1.1.m1.1.28.2.2.2.2.2" xref="p1.1.m1.1.28.2.2.2.2.2.cmml">
                <mi mathvariant="normal" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">Ψ</mi>
                <mn id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">1</mn>
              </msub>
            </mrow>
            <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.28.2.2.2.1.cmml">,</mo>
            <msub id="p1.1.m1.1.28.2.2.2.3" xref="p1.1.m1.1.28.2.2.2.3.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">Ψ</mi>
              <mn id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">2</mn>
            </msub>
            <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.28.2.2.2.1.cmml">)</mo>
          </mrow>
          <mo mathvariant="italic" separator="true" id="p1.1.m1.1.27" xref="p1.1.m1.1.28.2.2.1.cmml"> </mo>
          <mrow id="p1.1.m1.1.28.2.2.3" xref="p1.1.m1.1.28.2.2.3.cmml">
            <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">∀</mo>
            <msub id="p1.1.m1.1.28.2.2.3.1" xref="p1.1.m1.1.28.2.2.3.1.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">Ψ</mi>
              <mn id="p1.1.m1.1.21.1" xref="p1.1.m1.1.21.1.cmml">1</mn>
            </msub>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.28.1a.cmml">,</mo>
      <mrow id="p1.1.m1.1.28.3" xref="p1.1.m1.1.28.3.cmml">
        <msub id="p1.1.m1.1.28.3.1" xref="p1.1.m1.1.28.3.1.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">Ψ</mi>
          <mn id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">2</mn>
        </msub>
        <mo id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">∈</mo>
        <mi id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">H</mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.28.1.cmml" xref="p1.1.m1.1.28">
        <csymbol cd="ambiguous" id="p1.1.m1.1.28.1a.cmml" xref="p1.1.m1.1.22">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.28.2.cmml" xref="p1.1.m1.1.28.2">
          <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
          <interval closure="open" id="p1.1.m1.1.28.2.1.1.cmml" xref="p1.1.m1.1.28.2.1">
            <apply id="p1.1.m1.1.28.2.1.2.cmml" xref="p1.1.m1.1.28.2.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.1.2.1.cmml" xref="p1.1.m1.1.28.2.1.2">subscript</csymbol>
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">Ψ</ci>
              <cn type="integer" id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">1</cn>
            </apply>
            <apply id="p1.1.m1.1.28.2.1.3.cmml" xref="p1.1.m1.1.28.2.1.3">
              <times id="p1.1.m1.1.28.2.1.3.1.cmml" xref="p1.1.m1.1.28.2.1.3.1"/>
              <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">𝐹</ci>
              </apply>
              <apply id="p1.1.m1.1.28.2.1.3.2.cmml" xref="p1.1.m1.1.28.2.1.3.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.1.3.2.1.cmml" xref="p1.1.m1.1.28.2.1.3.2">subscript</csymbol>
                <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">Ψ</ci>
                <cn type="integer" id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">2</cn>
              </apply>
            </apply>
          </interval>
          <list id="p1.1.m1.1.28.2.2.1.cmml" xref="p1.1.m1.1.28.2.2">
            <interval closure="open" id="p1.1.m1.1.28.2.2.2.1.cmml" xref="p1.1.m1.1.28.2.2.2">
              <apply id="p1.1.m1.1.28.2.2.2.2.cmml" xref="p1.1.m1.1.28.2.2.2.2">
                <times id="p1.1.m1.1.28.2.2.2.2.1.cmml" xref="p1.1.m1.1.28.2.2.2.2.1"/>
                <apply id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">
                  <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1">^</ci>
                  <ci id="p1.1.m1.1.11.2.cmml" xref="p1.1.m1.1.11.2">𝐹</ci>
                </apply>
                <apply id="p1.1.m1.1.28.2.2.2.2.2.cmml" xref="p1.1.m1.1.28.2.2.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.2.2.2.1.cmml" xref="p1.1.m1.1.28.2.2.2.2.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">Ψ</ci>
                  <cn type="integer" id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">1</cn>
                </apply>
              </apply>
              <apply id="p1.1.m1.1.28.2.2.2.3.cmml" xref="p1.1.m1.1.28.2.2.2.3">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.2.3.1.cmml" xref="p1.1.m1.1.28.2.2.2.3">subscript</csymbol>
                <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">Ψ</ci>
                <cn type="integer" id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">2</cn>
              </apply>
            </interval>
            <apply id="p1.1.m1.1.28.2.2.3.cmml" xref="p1.1.m1.1.28.2.2.3">
              <csymbol cd="latexml" id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">for-all</csymbol>
              <apply id="p1.1.m1.1.28.2.2.3.1.cmml" xref="p1.1.m1.1.28.2.2.3.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.28.2.2.3.1.1.cmml" xref="p1.1.m1.1.28.2.2.3.1">subscript</csymbol>
                <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">Ψ</ci>
                <cn type="integer" id="p1.1.m1.1.21.1.cmml" xref="p1.1.m1.1.21.1">1</cn>
              </apply>
            </apply>
          </list>
        </apply>
        <apply id="p1.1.m1.1.28.3.cmml" xref="p1.1.m1.1.28.3">
          <in id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/>
          <apply id="p1.1.m1.1.28.3.1.cmml" xref="p1.1.m1.1.28.3.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.28.3.1.1.cmml" xref="p1.1.m1.1.28.3.1">subscript</csymbol>
            <ci id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23">Ψ</ci>
            <cn type="integer" id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">2</cn>
          </apply>
          <ci id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">𝐻</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left({{\Psi}_{1}},\hat{F}{{\Psi}_{2}}\right)=%
\left(\hat{F}{{\Psi}_{1}},{{\Psi}_{2}}\right)\quad\forall{{\Psi}_{1}},{{\Psi}_%
{2}}\in H}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (1.3 KB / 314 B) :

(Ψ1,F^Ψ2)=(F^Ψ1,Ψ2)∀Ψ1,Ψ2∈H
<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">(</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>F</mi><mo>^</mo></mover></mrow></mrow><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mspace width="1em"></mspace><mi mathvariant="normal">&#x2200;</mi><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>&#x2208;</mo><mi>H</mi></mstyle></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 Operatoren im Hilbertraum page

Identifiers

  • Ψ1
  • F^
  • Ψ2
  • F^
  • Ψ1
  • Ψ2
  • Ψ1
  • Ψ2
  • H

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"