– PhysikWiki

General

Display information for equation id:math.2413.22 on revision:2413

* Page found: Quantenmechanische Gleichgewichtsverteilungen (eq math.2413.22)

Occurrences on the following pages:

Quantenmechanische Gleichgewichtsverteilungen Eq: math.2413.22

Hash: cdff08f9b50c6eef3168dd598a14a9fc

TeX (original user input):

{{\left| \left\langle  \alpha   |  \Psi  \right\rangle  \right|}^{2}}=\left\langle  \Psi   |  \alpha  \right\rangle \left\langle  \alpha   |  \Psi  \right\rangle =\left\langle  \Psi  \right|{{\hat{P}}_{\alpha }}\left| \Psi  \right\rangle ={{P}_{\alpha }}

TeX (checked):

{{\left|\left\langle \alpha |\Psi \right\rangle \right|}^{2}}=\left\langle \Psi |\alpha \right\rangle \left\langle \alpha |\Psi \right\rangle =\left\langle \Psi \right|{{\hat {P}}_{\alpha }}\left|\Psi \right\rangle ={{P}_{\alpha }}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (7.533 KB / 1.299 KB) :

{\displaystyle{\displaystyle{{\left|\left\langle\alpha|\Psi\right\rangle\right% |}^{2}}=\left\langle\Psi|\alpha\right\rangle\left\langle\alpha|\Psi\right% \rangle=\left\langle\Psi\right|{{\hat{P}}_{\alpha}}\left|\Psi\right\rangle={{P% }_{\alpha}}}}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{{\left|\left\langle\alpha|\Psi\right\rangle\right%&#10;|}^{2}}=\left\langle\Psi|\alpha\right\rangle\left\langle\alpha|\Psi\right%&#10;\rangle=\left\langle\Psi\right|{{\hat{P}}_{\alpha}}\left|\Psi\right\rangle={{P%&#10;}_{\alpha}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">
      <msup id="p1.1.m1.1.32.2" xref="p1.1.m1.1.32.2.cmml">
        <mrow id="p1.1.m1.1.32.2.2" xref="p1.1.m1.1.32.2.2.1.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.32.2.2.1.1.cmml">|</mo>
          <mrow id="p1.1.m1.1.32.2.2.2" xref="p1.1.m1.1.32.2.2.2.1.cmml">
            <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.32.2.2.2.1.1.cmml">⟨</mo>
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">α</mi>
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.32.2.2.2.1.1.cmml">|</mo>
            <mi mathvariant="normal" id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">Ψ</mi>
            <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.32.2.2.2.1.1.cmml">⟩</mo>
          </mrow>
          <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.32.2.2.1.1.cmml">|</mo>
        </mrow>
        <mn id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">2</mn>
      </msup>
      <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">=</mo>
      <mrow id="p1.1.m1.1.32.3" xref="p1.1.m1.1.32.3.cmml">
        <mrow id="p1.1.m1.1.32.3.2" xref="p1.1.m1.1.32.3.2.1.cmml">
          <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.32.3.2.1.1.cmml">⟨</mo>
          <mi mathvariant="normal" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">Ψ</mi>
          <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.32.3.2.1.1.cmml">|</mo>
          <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">α</mi>
          <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.32.3.2.1.1.cmml">⟩</mo>
        </mrow>
        <mo id="p1.1.m1.1.32.3.1" xref="p1.1.m1.1.32.3.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.32.3.3" xref="p1.1.m1.1.32.3.3.1.cmml">
          <mo id="p1.1.m1.1.15" xref="p1.1.m1.1.32.3.3.1.1.cmml">⟨</mo>
          <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">α</mi>
          <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.32.3.3.1.1.cmml">|</mo>
          <mi mathvariant="normal" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">Ψ</mi>
          <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.32.3.3.1.1.cmml">⟩</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">=</mo>
      <mrow id="p1.1.m1.1.32.4" xref="p1.1.m1.1.32.4.1.cmml">
        <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.32.4.1.1.cmml">⟨</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">Ψ</mi>
        <mo fence="true" id="p1.1.m1.1.23" xref="p1.1.m1.1.32.4.1.1.cmml">|</mo>
        <msub id="p1.1.m1.1.32.4.2" xref="p1.1.m1.1.32.4.2.cmml">
          <mover accent="true" id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">
            <mi id="p1.1.m1.1.24.2" xref="p1.1.m1.1.24.2.cmml">P</mi>
            <mo stretchy="false" id="p1.1.m1.1.24.1" xref="p1.1.m1.1.24.1.cmml">^</mo>
          </mover>
          <mi id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">α</mi>
        </msub>
        <mo fence="true" id="p1.1.m1.1.26" xref="p1.1.m1.1.32.4.1.1.cmml">|</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">Ψ</mi>
        <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.32.4.1.1.cmml">⟩</mo>
      </mrow>
      <mo id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">=</mo>
      <msub id="p1.1.m1.1.32.5" xref="p1.1.m1.1.32.5.cmml">
        <mi id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">P</mi>
        <mi id="p1.1.m1.1.31.1" xref="p1.1.m1.1.31.1.cmml">α</mi>
      </msub>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">
        <and id="p1.1.m1.1.32a.cmml" xref="p1.1.m1.1.32"/>
        <apply id="p1.1.m1.1.32b.cmml" xref="p1.1.m1.1.32">
          <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
          <apply id="p1.1.m1.1.32.2.cmml" xref="p1.1.m1.1.32.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.32.2.1.cmml" xref="p1.1.m1.1.32.2">superscript</csymbol>
            <apply id="p1.1.m1.1.32.2.2.1.cmml" xref="p1.1.m1.1.32.2.2">
              <abs id="p1.1.m1.1.32.2.2.1.1.cmml" xref="p1.1.m1.1.1"/>
              <apply id="p1.1.m1.1.32.2.2.2.1.cmml" xref="p1.1.m1.1.32.2.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.32.2.2.2.1.1.cmml" xref="p1.1.m1.1.2">inner-product</csymbol>
                <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝛼</ci>
                <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">Ψ</ci>
              </apply>
            </apply>
            <cn type="integer" id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">2</cn>
          </apply>
          <apply id="p1.1.m1.1.32.3.cmml" xref="p1.1.m1.1.32.3">
            <times id="p1.1.m1.1.32.3.1.cmml" xref="p1.1.m1.1.32.3.1"/>
            <apply id="p1.1.m1.1.32.3.2.1.cmml" xref="p1.1.m1.1.32.3.2">
              <csymbol cd="latexml" id="p1.1.m1.1.32.3.2.1.1.cmml" xref="p1.1.m1.1.10">inner-product</csymbol>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">Ψ</ci>
              <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">𝛼</ci>
            </apply>
            <apply id="p1.1.m1.1.32.3.3.1.cmml" xref="p1.1.m1.1.32.3.3">
              <csymbol cd="latexml" id="p1.1.m1.1.32.3.3.1.1.cmml" xref="p1.1.m1.1.15">inner-product</csymbol>
              <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝛼</ci>
              <ci id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18">Ψ</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.32c.cmml" xref="p1.1.m1.1.32">
          <eq id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"/>
          <share href="#p1.1.m1.1.32.3.cmml" id="p1.1.m1.1.32d.cmml" xref="p1.1.m1.1.32"/>
          <apply id="p1.1.m1.1.32.4.1.cmml" xref="p1.1.m1.1.32.4">
            <csymbol cd="latexml" id="p1.1.m1.1.32.4.1.1.cmml" xref="p1.1.m1.1.21">quantum-operator-product</csymbol>
            <ci id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">Ψ</ci>
            <apply id="p1.1.m1.1.32.4.2.cmml" xref="p1.1.m1.1.32.4.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.32.4.2.1.cmml" xref="p1.1.m1.1.32.4.2">subscript</csymbol>
              <apply id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">
                <ci id="p1.1.m1.1.24.1.cmml" xref="p1.1.m1.1.24.1">^</ci>
                <ci id="p1.1.m1.1.24.2.cmml" xref="p1.1.m1.1.24.2">𝑃</ci>
              </apply>
              <ci id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">𝛼</ci>
            </apply>
            <ci id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">Ψ</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.32e.cmml" xref="p1.1.m1.1.32">
          <eq id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29"/>
          <share href="#p1.1.m1.1.32.4.cmml" id="p1.1.m1.1.32f.cmml" xref="p1.1.m1.1.32"/>
          <apply id="p1.1.m1.1.32.5.cmml" xref="p1.1.m1.1.32.5">
            <csymbol cd="ambiguous" id="p1.1.m1.1.32.5.1.cmml" xref="p1.1.m1.1.32.5">subscript</csymbol>
            <ci id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">𝑃</ci>
            <ci id="p1.1.m1.1.31.1.cmml" xref="p1.1.m1.1.31.1">𝛼</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{{\left|\left\langle\alpha|\Psi\right\rangle\right%
|}^{2}}=\left\langle\Psi|\alpha\right\rangle\left\langle\alpha|\Psi\right%
\rangle=\left\langle\Psi\right|{{\hat{P}}_{\alpha}}\left|\Psi\right\rangle={{P%
}_{\alpha}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (1.466 KB / 322 B) :

{| ⟨ α | Ψ ⟩ |}^{2} = ⟨ Ψ | α ⟩ ⟨ α | Ψ ⟩ = ⟨ Ψ | {\hat{P}}_{α} | Ψ ⟩ = P_{α}

<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><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi>&#x03B1;</mi><mo>|</mo><mi mathvariant="normal">&#x03A8;</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></mstyle><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi mathvariant="normal">&#x03A8;</mi><mo>|</mo><mi>&#x03B1;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x27E8;</mo><mi>&#x03B1;</mi><mo>|</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">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><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"><mi>&#x03B1;</mi></mrow></msub><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><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>&#x03B1;</mi></mrow></msub></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$α$

$Ψ$

$Ψ$

$α$

$α$

$Ψ$

$Ψ$

${\hat{P}}_{α}$

$Ψ$

$P_{α}$

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