Jump to navigation Jump to search

General

Display information for equation id:math.2711.17 on revision:2711

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.17)

(force rerendering)

Occurrences on the following pages:

Hash: 9a1d4147cd60144c59e25e2546850c76

TeX (original user input): 

\forall n,m>N\left( \varepsilon  \right)\Rightarrow \left\| {{\Psi }_{n}}-{{\Psi }_{m}} \right\|<\varepsilon

TeX (checked): 

\forall n,m>N\left(\varepsilon \right)\Rightarrow \left\|{{\Psi }_{n}}-{{\Psi }_{m}}\right\|<\varepsilon

LaTeXML (experimental; uses MathML) rendering

MathML (5.101 KB / 1.015 KB) :

∀ n , m > N ⁢ ( ε ) ⇒ ∥ Ψ n - Ψ m ∥ < ε for-all 𝑛 𝑚 𝑁 𝜀 ⇒ norm subscript Ψ 𝑛 subscript Ψ 𝑚 𝜀 {\displaystyle{\displaystyle\forall n,m>N\left(\varepsilon\right)\Rightarrow% \left\|{{\Psi}_{n}}-{{\Psi}_{m}}\right\|<\varepsilon}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\forall n,m&gt;N\left(\varepsilon\right)\Rightarrow%&#10;\left\|{{\Psi}_{n}}-{{\Psi}_{m}}\right\|&lt;\varepsilon}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">
      <mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.1.cmml">
        <mrow id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.20.2.2.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">∀</mo>
          <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">n</mi>
        </mrow>
        <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.20.2.1.cmml">,</mo>
        <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">m</mi>
      </mrow>
      <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">&gt;</mo>
      <mrow id="p1.1.m1.1.20.3" xref="p1.1.m1.1.20.3.cmml">
        <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">N</mi>
        <mo id="p1.1.m1.1.20.3.1" xref="p1.1.m1.1.20.3.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.20.3.2" xref="p1.1.m1.1.20.3.cmml">
          <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.20.3.cmml">(</mo>
          <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">ε</mi>
          <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.20.3.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">⇒</mo>
      <mrow id="p1.1.m1.1.20.4" xref="p1.1.m1.1.20.4.1.cmml">
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.20.4.1.1.cmml">∥</mo>
        <mrow id="p1.1.m1.1.20.4.2" xref="p1.1.m1.1.20.4.2.cmml">
          <msub id="p1.1.m1.1.20.4.2.1" xref="p1.1.m1.1.20.4.2.1.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">Ψ</mi>
            <mi id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">n</mi>
          </msub>
          <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">-</mo>
          <msub id="p1.1.m1.1.20.4.2.2" xref="p1.1.m1.1.20.4.2.2.cmml">
            <mi mathvariant="normal" id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">Ψ</mi>
            <mi id="p1.1.m1.1.16.1" xref="p1.1.m1.1.16.1.cmml">m</mi>
          </msub>
        </mrow>
        <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.20.4.1.1.cmml">∥</mo>
      </mrow>
      <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">&lt;</mo>
      <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">ε</mi>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">
        <and id="p1.1.m1.1.20a.cmml" xref="p1.1.m1.1.20"/>
        <apply id="p1.1.m1.1.20b.cmml" xref="p1.1.m1.1.20">
          <gt id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <list id="p1.1.m1.1.20.2.1.cmml" xref="p1.1.m1.1.20.2">
            <apply id="p1.1.m1.1.20.2.2.cmml" xref="p1.1.m1.1.20.2.2">
              <csymbol cd="latexml" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">for-all</csymbol>
              <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝑛</ci>
            </apply>
            <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑚</ci>
          </list>
          <apply id="p1.1.m1.1.20.3.cmml" xref="p1.1.m1.1.20.3">
            <times id="p1.1.m1.1.20.3.1.cmml" xref="p1.1.m1.1.20.3.1"/>
            <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑁</ci>
            <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝜀</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.20c.cmml" xref="p1.1.m1.1.20">
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">⇒</ci>
          <share href="#p1.1.m1.1.20.3.cmml" id="p1.1.m1.1.20d.cmml" xref="p1.1.m1.1.20"/>
          <apply id="p1.1.m1.1.20.4.1.cmml" xref="p1.1.m1.1.20.4">
            <csymbol cd="latexml" id="p1.1.m1.1.20.4.1.1.cmml" xref="p1.1.m1.1.11">norm</csymbol>
            <apply id="p1.1.m1.1.20.4.2.cmml" xref="p1.1.m1.1.20.4.2">
              <minus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
              <apply id="p1.1.m1.1.20.4.2.1.cmml" xref="p1.1.m1.1.20.4.2.1">
                <csymbol cd="ambiguous" id="p1.1.m1.1.20.4.2.1.1.cmml" xref="p1.1.m1.1.20.4.2.1">subscript</csymbol>
                <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">Ψ</ci>
                <ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">𝑛</ci>
              </apply>
              <apply id="p1.1.m1.1.20.4.2.2.cmml" xref="p1.1.m1.1.20.4.2.2">
                <csymbol cd="ambiguous" id="p1.1.m1.1.20.4.2.2.1.cmml" xref="p1.1.m1.1.20.4.2.2">subscript</csymbol>
                <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">Ψ</ci>
                <ci id="p1.1.m1.1.16.1.cmml" xref="p1.1.m1.1.16.1">𝑚</ci>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.20e.cmml" xref="p1.1.m1.1.20">
          <lt id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"/>
          <share href="#p1.1.m1.1.20.4.cmml" id="p1.1.m1.1.20f.cmml" xref="p1.1.m1.1.20"/>
          <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝜀</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\forall n,m&gt;N\left(\varepsilon\right)\Rightarrow%
\left\|{{\Psi}_{n}}-{{\Psi}_{m}}\right\|&lt;\varepsilon}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (773 B / 301 B) :

∀n,m>N(ε)⇒‖Ψn−Ψm‖<ε
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi mathvariant="normal">&#x2200;</mi><mi>n</mi><mo>,</mo><mi>m</mi><mo>&gt;</mo><mi>N</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>&#x03B5;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x21D2;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">&#x2016;</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo>&#x2212;</mo><msub><mi mathvariant="normal">&#x03A8;</mi><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msub><mo data-mjx-texclass="CLOSE">&#x2016;</mo></mrow><mo>&lt;</mo><mi>&#x03B5;</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 Formaler Aufbau der Quantenmechanik page

Identifiers

  • n
  • m
  • N
  • ε
  • Ψn
  • Ψm
  • ε

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"