Jump to navigation Jump to search

General

Display information for equation id:math.1985.51 on revision:1985

* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1985.51)

(force rerendering)

Occurrences on the following pages:

Hash: e63013eda10eead6c56c274a3b37c7fb

TeX (original user input): 

\left( \frac{-{{\hbar }^{2}}}{2m}\Delta +V(\bar{r}) \right)\Psi (\bar{r})=E\Psi (\bar{r})

TeX (checked): 

\left({\frac {-{{\hbar }^{2}}}{2m}}\Delta +V({\bar {r}})\right)\Psi ({\bar {r}})=E\Psi ({\bar {r}})

LaTeXML (experimental; uses MathML) rendering

MathML (7.698 KB / 1.29 KB) :

( - ℏ 2 2 ⁢ m ⁢ Δ + V ⁢ ( r ¯ ) ) ⁢ Ψ ⁢ ( r ¯ ) = E ⁢ Ψ ⁢ ( r ¯ ) superscript Planck-constant-over-2-pi 2 2 𝑚 Δ 𝑉 ¯ 𝑟 Ψ ¯ 𝑟 𝐸 Ψ ¯ 𝑟 {\displaystyle{\displaystyle\left(\frac{-{{\hbar}^{2}}}{2m}\Delta+V(\bar{r})% \right)\Psi(\bar{r})=E\Psi(\bar{r})}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle\left(\frac{-{{\hbar}^{2}}}{2m}\Delta+V(\bar{r})%&#10;\right)\Psi(\bar{r})=E\Psi(\bar{r})}}" 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.m1.1.20.1" xref="p1.1.m1.1.20.1.cmml">
        <mrow id="p1.1.m1.1.20.1.2" xref="p1.1.m1.1.20.1.2.2.cmml">
          <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.20.1.2.2.cmml">(</mo>
          <mrow id="p1.1.m1.1.20.1.2.2" xref="p1.1.m1.1.20.1.2.2.cmml">
            <mrow id="p1.1.m1.1.20.1.2.2.1" xref="p1.1.m1.1.20.1.2.2.1.cmml">
              <mstyle displaystyle="true" id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">
                <mfrac id="p1.1.m1.1.2a" xref="p1.1.m1.1.2.cmml">
                  <mrow id="p1.1.m1.1.2.2" xref="p1.1.m1.1.2.2.cmml">
                    <mo id="p1.1.m1.1.2.2.1" xref="p1.1.m1.1.2.2.1.cmml">-</mo>
                    <msup id="p1.1.m1.1.2.2.4" xref="p1.1.m1.1.2.2.4.cmml">
                      <mi mathvariant="normal" id="p1.1.m1.1.2.2.2" xref="p1.1.m1.1.2.2.2.cmml">ℏ</mi>
                      <mn id="p1.1.m1.1.2.2.3.1" xref="p1.1.m1.1.2.2.3.1.cmml">2</mn>
                    </msup>
                  </mrow>
                  <mrow id="p1.1.m1.1.2.3" xref="p1.1.m1.1.2.3.cmml">
                    <mn id="p1.1.m1.1.2.3.1" xref="p1.1.m1.1.2.3.1.cmml">2</mn>
                    <mo id="p1.1.m1.1.2.3.3" xref="p1.1.m1.1.2.3.3.cmml">⁢</mo>
                    <mi id="p1.1.m1.1.2.3.2" xref="p1.1.m1.1.2.3.2.cmml">m</mi>
                  </mrow>
                </mfrac>
              </mstyle>
              <mo id="p1.1.m1.1.20.1.2.2.1.1" xref="p1.1.m1.1.20.1.2.2.1.1.cmml">⁢</mo>
              <mi mathvariant="normal" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">Δ</mi>
            </mrow>
            <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">+</mo>
            <mrow id="p1.1.m1.1.20.1.2.2.2" xref="p1.1.m1.1.20.1.2.2.2.cmml">
              <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">V</mi>
              <mo id="p1.1.m1.1.20.1.2.2.2.1" xref="p1.1.m1.1.20.1.2.2.2.1.cmml">⁢</mo>
              <mrow id="p1.1.m1.1.20.1.2.2.2.2" xref="p1.1.m1.1.7.cmml">
                <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.7.cmml">(</mo>
                <mover accent="true" id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">
                  <mi id="p1.1.m1.1.7.2" xref="p1.1.m1.1.7.2.cmml">r</mi>
                  <mo stretchy="false" id="p1.1.m1.1.7.1" xref="p1.1.m1.1.7.1.cmml">¯</mo>
                </mover>
                <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.7.cmml">)</mo>
              </mrow>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.20.1.2.2.cmml">)</mo>
        </mrow>
        <mo id="p1.1.m1.1.20.1.1" xref="p1.1.m1.1.20.1.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">Ψ</mi>
        <mo id="p1.1.m1.1.20.1.1a" xref="p1.1.m1.1.20.1.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.20.1.3" xref="p1.1.m1.1.12.cmml">
          <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.12.cmml">(</mo>
          <mover accent="true" id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
            <mi id="p1.1.m1.1.12.2" xref="p1.1.m1.1.12.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">¯</mo>
          </mover>
          <mo stretchy="false" id="p1.1.m1.1.13" xref="p1.1.m1.1.12.cmml">)</mo>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">=</mo>
      <mrow id="p1.1.m1.1.20.2" xref="p1.1.m1.1.20.2.cmml">
        <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">E</mi>
        <mo id="p1.1.m1.1.20.2.1" xref="p1.1.m1.1.20.2.1.cmml">⁢</mo>
        <mi mathvariant="normal" id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">Ψ</mi>
        <mo id="p1.1.m1.1.20.2.1a" xref="p1.1.m1.1.20.2.1.cmml">⁢</mo>
        <mrow id="p1.1.m1.1.20.2.2" xref="p1.1.m1.1.18.cmml">
          <mo stretchy="false" id="p1.1.m1.1.17" xref="p1.1.m1.1.18.cmml">(</mo>
          <mover accent="true" id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">
            <mi id="p1.1.m1.1.18.2" xref="p1.1.m1.1.18.2.cmml">r</mi>
            <mo stretchy="false" id="p1.1.m1.1.18.1" xref="p1.1.m1.1.18.1.cmml">¯</mo>
          </mover>
          <mo stretchy="false" id="p1.1.m1.1.19" xref="p1.1.m1.1.18.cmml">)</mo>
        </mrow>
      </mrow>
    </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">
        <eq id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
        <apply id="p1.1.m1.1.20.1.cmml" xref="p1.1.m1.1.20.1">
          <times id="p1.1.m1.1.20.1.1.cmml" xref="p1.1.m1.1.20.1.1"/>
          <apply id="p1.1.m1.1.20.1.2.2.cmml" xref="p1.1.m1.1.20.1.2">
            <plus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/>
            <apply id="p1.1.m1.1.20.1.2.2.1.cmml" xref="p1.1.m1.1.20.1.2.2.1">
              <times id="p1.1.m1.1.20.1.2.2.1.1.cmml" xref="p1.1.m1.1.20.1.2.2.1.1"/>
              <apply id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">
                <divide id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2"/>
                <apply id="p1.1.m1.1.2.2.cmml" xref="p1.1.m1.1.2.2">
                  <minus id="p1.1.m1.1.2.2.1.cmml" xref="p1.1.m1.1.2.2.1"/>
                  <apply id="p1.1.m1.1.2.2.4.cmml" xref="p1.1.m1.1.2.2.4">
                    <csymbol cd="ambiguous" id="p1.1.m1.1.2.2.4.1.cmml" xref="p1.1.m1.1.2.2.4">superscript</csymbol>
                    <csymbol cd="latexml" id="p1.1.m1.1.2.2.2.cmml" xref="p1.1.m1.1.2.2.2">Planck-constant-over-2-pi</csymbol>
                    <cn type="integer" id="p1.1.m1.1.2.2.3.1.cmml" xref="p1.1.m1.1.2.2.3.1">2</cn>
                  </apply>
                </apply>
                <apply id="p1.1.m1.1.2.3.cmml" xref="p1.1.m1.1.2.3">
                  <times id="p1.1.m1.1.2.3.3.cmml" xref="p1.1.m1.1.2.3.3"/>
                  <cn type="integer" id="p1.1.m1.1.2.3.1.cmml" xref="p1.1.m1.1.2.3.1">2</cn>
                  <ci id="p1.1.m1.1.2.3.2.cmml" xref="p1.1.m1.1.2.3.2">𝑚</ci>
                </apply>
              </apply>
              <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">Δ</ci>
            </apply>
            <apply id="p1.1.m1.1.20.1.2.2.2.cmml" xref="p1.1.m1.1.20.1.2.2.2">
              <times id="p1.1.m1.1.20.1.2.2.2.1.cmml" xref="p1.1.m1.1.20.1.2.2.2.1"/>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑉</ci>
              <apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.20.1.2.2.2.2">
                <ci id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7.1">¯</ci>
                <ci id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">𝑟</ci>
              </apply>
            </apply>
          </apply>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">Ψ</ci>
          <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.20.1.3">
            <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">¯</ci>
            <ci id="p1.1.m1.1.12.2.cmml" xref="p1.1.m1.1.12.2">𝑟</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.20.2.cmml" xref="p1.1.m1.1.20.2">
          <times id="p1.1.m1.1.20.2.1.cmml" xref="p1.1.m1.1.20.2.1"/>
          <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝐸</ci>
          <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">Ψ</ci>
          <apply id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.20.2.2">
            <ci id="p1.1.m1.1.18.1.cmml" xref="p1.1.m1.1.18.1">¯</ci>
            <ci id="p1.1.m1.1.18.2.cmml" xref="p1.1.m1.1.18.2">𝑟</ci>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\displaystyle\left(\frac{-{{\hbar}^{2}}}{2m}\Delta+V(\bar{r})%
\right)\Psi(\bar{r})=E\Psi(\bar{r})}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


SVG (MathML can be enabled via browser plugin) rendering

MathML (2.515 KB / 576 B) :

( − ℏ 2 2 m Δ + V ( r ¯ ) ) Ψ ( r ¯ ) = E Ψ ( r ¯ ) {\displaystyle \left({\frac {-{{\hbar }^{2}}}{2m}}\Delta +V({\bar {r}})\right)\Psi ({\bar {r}})=E\Psi ({\bar {r}})} 
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \left({\frac {-{{\hbar }^{2}}}{2m}}\Delta +V({\bar {r}})\right)\Psi ({\bar {r}})=E\Psi ({\bar {r}})}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow>
          <mo>(</mo>
          <mrow>
            <mrow class="MJX-TeXAtom-ORD">
              <mfrac>
                <mrow>
                  <mo>&#x2212;<!-- − --></mo>
                  <mrow class="MJX-TeXAtom-ORD">
                    <msup>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mi class="MJX-variant">&#x210F;<!-- ℏ --></mi>
                      </mrow>
                      <mrow class="MJX-TeXAtom-ORD">
                        <mn>2</mn>
                      </mrow>
                    </msup>
                  </mrow>
                </mrow>
                <mrow>
                  <mn>2</mn>
                  <mi>m</mi>
                </mrow>
              </mfrac>
            </mrow>
            <mi mathvariant="normal">&#x0394;<!-- Δ --></mi>
            <mo>+</mo>
            <mi>V</mi>
            <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>
          </mrow>
          <mo>)</mo>
        </mrow>
        <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
        <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>
        <mi>E</mi>
        <mi mathvariant="normal">&#x03A8;<!-- Ψ --></mi>
        <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>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \left({\frac {-{{\hbar }^{2}}}{2m}}\Delta +V({\bar {r}})\right)\Psi ({\bar {r}})=E\Psi ({\bar {r}})}</annotation>
  </semantics>
</math>

SVG (9.336 KB / 3.887 KB) :

{\displaystyle \left({\frac {-{{\hbar }^{2}}}{2m}}\Delta +V({\bar {r}})\right)\Psi ({\bar {r}})=E\Psi ({\bar {r}})}

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 Hamilton-Jacobische Differenzialgleichung 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"