Jump to navigation Jump to search

General

Display information for equation id:math.1796.16 on revision:1796

* Page found: Drehimpulsdarstellung und Streuphasen (eq math.1796.16)

(force rerendering)

Occurrences on the following pages:

Hash: 04bdb079453d701365c3d95daac0a16c

TeX (original user input): 

{{\Psi }_{e}}(\bar{r})=\sum\limits_{l=0}^{\infty }{{}}\frac{1}{r}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )

TeX (checked): 

{{\Psi }_{e}}({\bar {r}})=\sum \limits _{l=0}^{\infty }{}{\frac {1}{r}}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )

LaTeXML (experimental; uses MathML) rendering

MathML (7.572 KB / 1.354 KB) :

Ψ e ⁢ ( r ¯ ) = ∑ l = 0 ∞ 1 r ⁢ u l ⁢ ( r ) ⁢ P l ⁢ ( cos ⁡ ϑ ) subscript Ψ 𝑒 ¯ 𝑟 superscript subscript 𝑙 0 1 𝑟 subscript 𝑢 𝑙 𝑟 subscript 𝑃 𝑙 italic-ϑ {\displaystyle{\displaystyle{{\Psi}_{e}}(\bar{r})=\sum\limits_{l=0}^{\infty}{{% }}\frac{1}{r}{{u}_{l}}(r){{P}_{l}}(\cos\vartheta)}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{{\Psi}_{e}}(\bar{r})=\sum\limits_{l=0}^{\infty}{{%&#10;}}\frac{1}{r}{{u}_{l}}(r){{P}_{l}}(\cos\vartheta)}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">
      <mrow id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">
        <msub id="p1.1.m1.1.22.1.2" xref="p1.1.m1.1.22.1.2.cmml">
          <mi mathvariant="normal" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">Ψ</mi>
          <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">e</mi>
        </msub>
        <mo id="p1.1.m1.1.22.1.1" xref="p1.1.m1.1.22.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.22.1.3" xref="p1.1.m1.1.4.cmml">
          <mo stretchy="false" id="p1.1.m1.1.3" xref="p1.1.m1.1.4.cmml">(</mo>
          <mover accent="true" id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">
            <mi id="p1.1.m1.1.4.2" xref="p1.1.m1.1.4.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">¯</mo>
          </mover>
          <mo stretchy="false" id="p1.1.m1.1.5" xref="p1.1.m1.1.4.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">=</mo>
      <mrow id="p1.1.m1.1.22.2" xref="p1.1.m1.1.22.2.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.22.2.1" xref="p1.1.m1.1.22.2.1.cmml">
          <munderover id="p1.1.m1.1.22.2.1a" xref="p1.1.m1.1.22.2.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">∑</mo>
            <mrow id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">
              <mi id="p1.1.m1.1.8.1.1" xref="p1.1.m1.1.8.1.1.cmml">l</mi>
              <mo id="p1.1.m1.1.8.1.2" xref="p1.1.m1.1.8.1.2.cmml">=</mo>
              <mn id="p1.1.m1.1.8.1.3" xref="p1.1.m1.1.8.1.3.cmml">0</mn>
            </mrow>
            <mi mathvariant="normal" id="p1.1.m1.1.9.1" xref="p1.1.m1.1.9.1.cmml">∞</mi>
          </munderover>
        </mstyle>
        <mrow id="p1.1.m1.1.22.2.2" xref="p1.1.m1.1.22.2.2.cmml">
          <mstyle displaystyle="true" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">
            <mfrac id="p1.1.m1.1.10a" xref="p1.1.m1.1.10.cmml">
              <mn id="p1.1.m1.1.10.2" xref="p1.1.m1.1.10.2.cmml">1</mn>
              <mi id="p1.1.m1.1.10.3" xref="p1.1.m1.1.10.3.cmml">r</mi>
            </mfrac>
          </mstyle>
          <mo id="p1.1.m1.1.22.2.2.1" xref="p1.1.m1.1.22.2.2.1.cmml">⁢</mo>
          <msub id="p1.1.m1.1.22.2.2.2" xref="p1.1.m1.1.22.2.2.2.cmml">
            <mi id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">u</mi>
            <mi id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">l</mi>
          </msub>
          <mo id="p1.1.m1.1.22.2.2.1a" xref="p1.1.m1.1.22.2.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.22.2.2.3" xref="p1.1.m1.1.22.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.22.2.2.cmml">(</mo>
            <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.22.2.2.cmml">)</mo>
          </mrow>
          <mo id="p1.1.m1.1.22.2.2.1b" xref="p1.1.m1.1.22.2.2.1.cmml">⁢</mo>
          <msub id="p1.1.m1.1.22.2.2.4" xref="p1.1.m1.1.22.2.2.4.cmml">
            <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">P</mi>
            <mi id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">l</mi>
          </msub>
          <mo id="p1.1.m1.1.22.2.2.1c" xref="p1.1.m1.1.22.2.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.22.2.2.5" xref="p1.1.m1.1.22.2.2.5.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.22.2.2.5.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.22.2.2.5.2" xref="p1.1.m1.1.22.2.2.5.2.cmml">
              <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">cos</mi>
              <mo id="p1.1.m1.1.22.2.2.5.2a" xref="p1.1.m1.1.22.2.2.5.2.cmml">⁡</mo>
              <mi id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">ϑ</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.21" xref="p1.1.m1.1.22.2.2.5.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">
        <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/>
        <apply id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">
          <times id="p1.1.m1.1.22.1.1.cmml" xref="p1.1.m1.1.22.1.1"/>
          <apply id="p1.1.m1.1.22.1.2.cmml" xref="p1.1.m1.1.22.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.22.1.2.1.cmml" xref="p1.1.m1.1.22.1.2">subscript</csymbol>
            <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">Ψ</ci>
            <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑒</ci>
          </apply>
          <apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.22.1.3">
            <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">¯</ci>
            <ci id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2">𝑟</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.22.2.cmml" xref="p1.1.m1.1.22.2">
          <apply id="p1.1.m1.1.22.2.1.cmml" xref="p1.1.m1.1.22.2.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.22.2.1.1.cmml" xref="p1.1.m1.1.22.2.1">superscript</csymbol>
            <apply id="p1.1.m1.1.22.2.1.2.cmml" xref="p1.1.m1.1.22.2.1">
              <csymbol cd="ambiguous" id="p1.1.m1.1.22.2.1.2.1.cmml" xref="p1.1.m1.1.22.2.1">subscript</csymbol>
              <sum id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
              <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">
                <eq id="p1.1.m1.1.8.1.2.cmml" xref="p1.1.m1.1.8.1.2"/>
                <ci id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.1.1">𝑙</ci>
                <cn type="integer" id="p1.1.m1.1.8.1.3.cmml" xref="p1.1.m1.1.8.1.3">0</cn>
              </apply>
            </apply>
            <infinity id="p1.1.m1.1.9.1.cmml" xref="p1.1.m1.1.9.1"/>
          </apply>
          <apply id="p1.1.m1.1.22.2.2.cmml" xref="p1.1.m1.1.22.2.2">
            <times id="p1.1.m1.1.22.2.2.1.cmml" xref="p1.1.m1.1.22.2.2.1"/>
            <apply id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">
              <divide id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10"/>
              <cn type="integer" id="p1.1.m1.1.10.2.cmml" xref="p1.1.m1.1.10.2">1</cn>
              <ci id="p1.1.m1.1.10.3.cmml" xref="p1.1.m1.1.10.3">𝑟</ci>
            </apply>
            <apply id="p1.1.m1.1.22.2.2.2.cmml" xref="p1.1.m1.1.22.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.22.2.2.2.1.cmml" xref="p1.1.m1.1.22.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝑢</ci>
              <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">𝑙</ci>
            </apply>
            <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑟</ci>
            <apply id="p1.1.m1.1.22.2.2.4.cmml" xref="p1.1.m1.1.22.2.2.4">
              <csymbol cd="ambiguous" id="p1.1.m1.1.22.2.2.4.1.cmml" xref="p1.1.m1.1.22.2.2.4">subscript</csymbol>
              <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑃</ci>
              <ci id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">𝑙</ci>
            </apply>
            <apply id="p1.1.m1.1.22.2.2.5.2.cmml" xref="p1.1.m1.1.22.2.2.5">
              <cos id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
              <ci id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20">italic-ϑ</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle{{\Psi}_{e}}(\bar{r})=\sum\limits_{l=0}^{\infty}{{%
}}\frac{1}{r}{{u}_{l}}(r){{P}_{l}}(\cos\vartheta)}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (2.453 KB / 599 B) :

Ψ e ( r ¯ ) = ∑ l = 0 ∞ 1 r u l ( r ) P l ( cos ⁡ ϑ ) {\displaystyle {{\Psi }_{e}}({\bar {r}})=\sum \limits _{l=0}^{\infty }{}{\frac {1}{r}}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {{\Psi }_{e}}({\bar {r}})=\sum \limits _{l=0}^{\infty }{}{\frac {1}{r}}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <msub>
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
            </mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>e</mi>
            </mrow>
          </msub>
        </mrow>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>r</mi>
              <mo stretchy="false">&#x00AF;<!-- ¯ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <munderover>
          <mo movablelimits="false">&#x2211;<!-- ∑ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>l</mi>
            <mo>=</mo>
            <mn>0</mn>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
          </mrow>
        </munderover>
        <mrow class="MJX-TeXAtom-ORD">

        </mrow>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mn>1</mn>
            <mi>r</mi>
          </mfrac>
        </mrow>
        <mrow class="MJX-TeXAtom-ORD">
          <msub>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>u</mi>
            </mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>l</mi>
            </mrow>
          </msub>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>r</mi>
        <mo stretchy="false">)</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <msub>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>P</mi>
            </mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mi>l</mi>
            </mrow>
          </msub>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>cos</mi>
        <mo>&#x2061;<!-- ⁡ --></mo>
        <mi>&#x03D1;<!-- ϑ --></mi>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {{\Psi }_{e}}({\bar {r}})=\sum \limits _{l=0}^{\infty }{}{\frac {1}{r}}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )}</annotation>
  </semantics>
</math>

SVG (10.591 KB / 4.463 KB) :

{\displaystyle {{\Psi }_{e}}({\bar {r}})=\sum \limits _{l=0}^{\infty }{}{\frac {1}{r}}{{u}_{l}}(r){{P}_{l}}(\cos \vartheta )}

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 Drehimpulsdarstellung und Streuphasen page

Identifiers

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"