Zur Navigation springen Zur Suche springen

General

Display information for equation id:math.2711.37 on revision:2711

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.37)

(force rerendering)

Occurrences on the following pages:

Hash: 0725e1b47cbaebe137bfacc5f79dd07c

TeX (original user input):

\Phi =\sum\limits_{n}{\left\langle  {{\Psi }_{n}} | \Phi  \right\rangle {{\Psi }_{n}}\quad \forall \Phi \in \mathcal{H}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (5.461 KB / 1.09 KB) :

Φ = n Ψ n | Φ Ψ n Φ formulae-sequence Φ subscript 𝑛 inner-product subscript Ψ 𝑛 Φ subscript Ψ 𝑛 for-all Φ {\displaystyle{\displaystyle\Phi=\sum\limits_{n}{\left\langle{{\Psi}_{n}}|\Phi% \right\rangle{{\Psi}_{n}}\quad\forall\Phi\in\mathcal{H}}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\Phi=\sum\limits_{n}{\left\langle{{\Psi}_{n}}|\Phi%&#10;\right\rangle{{\Psi}_{n}}\quad\forall\Phi\in\mathcal{H}}}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.19" xref="p1.1.m1.1.19.1.cmml">
      <mrow id="p1.1.m1.1.19.2" xref="p1.1.m1.1.19.2.cmml">
        <mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Φ</mi>
        <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
        <mrow id="p1.1.m1.1.19.2.1" xref="p1.1.m1.1.19.2.1.cmml">
          <mstyle displaystyle="true" id="p1.1.m1.1.19.2.1.1" xref="p1.1.m1.1.19.2.1.1.cmml">
            <munder id="p1.1.m1.1.19.2.1.1a" xref="p1.1.m1.1.19.2.1.1.cmml">
              <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml"></mo>
              <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">n</mi>
            </munder>
          </mstyle>
          <mrow id="p1.1.m1.1.19.2.1.2" xref="p1.1.m1.1.19.2.1.2.cmml">
            <mrow id="p1.1.m1.1.19.2.1.2.2" xref="p1.1.m1.1.19.2.1.2.2.1.cmml">
              <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.19.2.1.2.2.1.1.cmml"></mo>
              <msub id="p1.1.m1.1.19.2.1.2.2.2" xref="p1.1.m1.1.19.2.1.2.2.2.cmml">
                <mi mathvariant="normal" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">Ψ</mi>
                <mi id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">n</mi>
              </msub>
              <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.19.2.1.2.2.1.1.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.m1.1.19.2.1.2.2.1.1.cmml"></mo>
            </mrow>
            <mo id="p1.1.m1.1.19.2.1.2.1" xref="p1.1.m1.1.19.2.1.2.1.cmml"></mo>
            <msub id="p1.1.m1.1.19.2.1.2.3" xref="p1.1.m1.1.19.2.1.2.3.cmml">
              <mi mathvariant="normal" id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">Ψ</mi>
              <mi id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">n</mi>
            </msub>
          </mrow>
        </mrow>
      </mrow>
      <mo mathvariant="italic" separator="true" id="p1.1.m1.1.18" xref="p1.1.m1.1.19.1a.cmml"></mo>
      <mrow id="p1.1.m1.1.19.3" xref="p1.1.m1.1.19.3.cmml">
        <mrow id="p1.1.m1.1.19.3.1" xref="p1.1.m1.1.19.3.1.cmml">
          <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml"></mo>
          <mi mathvariant="normal" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">Φ</mi>
        </mrow>
        <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml"></mo>
        <mi class="ltx_font_mathcaligraphic" id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml"></mi>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.19.1.cmml" xref="p1.1.m1.1.19">
        <csymbol cd="ambiguous" id="p1.1.m1.1.19.1a.cmml" xref="p1.1.m1.1.18">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.19.2.cmml" xref="p1.1.m1.1.19.2">
          <eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
          <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Φ</ci>
          <apply id="p1.1.m1.1.19.2.1.cmml" xref="p1.1.m1.1.19.2.1">
            <apply id="p1.1.m1.1.19.2.1.1.cmml" xref="p1.1.m1.1.19.2.1.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.1.1.1.cmml" xref="p1.1.m1.1.19.2.1.1">subscript</csymbol>
              <sum id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
              <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">𝑛</ci>
            </apply>
            <apply id="p1.1.m1.1.19.2.1.2.cmml" xref="p1.1.m1.1.19.2.1.2">
              <times id="p1.1.m1.1.19.2.1.2.1.cmml" xref="p1.1.m1.1.19.2.1.2.1"/>
              <apply id="p1.1.m1.1.19.2.1.2.2.1.cmml" xref="p1.1.m1.1.19.2.1.2.2">
                <csymbol cd="latexml" id="p1.1.m1.1.19.2.1.2.2.1.1.cmml" xref="p1.1.m1.1.5">inner-product</csymbol>
                <apply id="p1.1.m1.1.19.2.1.2.2.2.cmml" xref="p1.1.m1.1.19.2.1.2.2.2">
                  <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.1.2.2.2.1.cmml" xref="p1.1.m1.1.19.2.1.2.2.2">subscript</csymbol>
                  <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">Ψ</ci>
                  <ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">𝑛</ci>
                </apply>
                <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">Φ</ci>
              </apply>
              <apply id="p1.1.m1.1.19.2.1.2.3.cmml" xref="p1.1.m1.1.19.2.1.2.3">
                <csymbol cd="ambiguous" id="p1.1.m1.1.19.2.1.2.3.1.cmml" xref="p1.1.m1.1.19.2.1.2.3">subscript</csymbol>
                <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">Ψ</ci>
                <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">𝑛</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.19.3.cmml" xref="p1.1.m1.1.19.3">
          <in id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
          <apply id="p1.1.m1.1.19.3.1.cmml" xref="p1.1.m1.1.19.3.1">
            <csymbol cd="latexml" id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">for-all</csymbol>
            <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">Φ</ci>
          </apply>
          <ci id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"></ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\Phi=\sum\limits_{n}{\left\langle{{\Psi}_{n}}|\Phi%
\right\rangle{{\Psi}_{n}}\quad\forall\Phi\in\mathcal{H}}}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML kann über ein Browser-Plugin aktiviert werden) rendering

MathML (2.207 KB / 590 B) :

Φ = n Ψ n | Φ Ψ n Φ H {\displaystyle \Phi =\sum \limits _{n}{\left\langle {{\Psi }_{n}}|\Phi \right\rangle {{\Psi }_{n}}\quad \forall \Phi \in {\mathcal {H}}}}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \Phi =\sum \limits _{n}{\left\langle {{\Psi }_{n}}|\Phi \right\rangle {{\Psi }_{n}}\quad \forall \Phi \in {\mathcal {H}}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi mathvariant="normal">&#x03A6;<!-- Φ --></mi>
        <mo>=</mo>
        <munder>
          <mo movablelimits="false">&#x2211;<!-- ∑ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>n</mi>
          </mrow>
        </munder>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow>
            <mo>&#x27E8;</mo>
            <mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <msub>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
                  </mrow>
                  <mrow class="MJX-TeXAtom-ORD">
                    <mi>n</mi>
                  </mrow>
                </msub>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mo stretchy="false">|</mo>
              </mrow>
              <mi mathvariant="normal">&#x03A6;<!-- Φ --></mi>
            </mrow>
            <mo>&#x27E9;</mo>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <msub>
              <mrow class="MJX-TeXAtom-ORD">
                <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
              </mrow>
              <mrow class="MJX-TeXAtom-ORD">
                <mi>n</mi>
              </mrow>
            </msub>
          </mrow>
          <mspace width="1em" />
          <mi mathvariant="normal">&#x2200;<!-- ∀ --></mi>
          <mi mathvariant="normal">&#x03A6;<!-- Φ --></mi>
          <mo>&#x2208;<!-- ∈ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mrow class="MJX-TeXAtom-ORD">
              <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi>
            </mrow>
          </mrow>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \Phi =\sum \limits _{n}{\left\langle {{\Psi }_{n}}|\Phi \right\rangle {{\Psi }_{n}}\quad \forall \Phi \in {\mathcal {H}}}}</annotation>
  </semantics>
</math>

SVG (6.607 KB / 2.927 KB) :

{\displaystyle \Phi =\sum \limits _{n}{\left\langle {{\Psi }_{n}}|\Phi \right\rangle {{\Psi }_{n}}\quad \forall \Phi \in {\mathcal {H}}}}

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

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results