- testwiki

General

Display information for equation id:math.1593.1 on revision:1593

* Page found: Kontinuitätsgleichung (Quantenmechnik) (eq math.1593.1)

Occurrences on the following pages:

Kontinuitätsgleichung (Quantenmechnik) Eq: math.1594.1

Hash: 664220a9cf8b72767f898c49655c7efc

TeX (original user input):

\begin{align}

& i\hbar \dot{\Psi }(\bar{r},t)=\frac{1}{2m}\left( \frac{\hbar }{i}\nabla -e\bar{A} \right)\left( \frac{\hbar }{i}\nabla -e\bar{A} \right)\Psi (\bar{r},t)+V\Psi (\bar{r},t) \\

& =\frac{1}{2m}\left[ -{{\hbar }^{2}}\Delta \Psi +i\hbar e\nabla \left( \bar{A}\Psi  \right)+i\hbar e\bar{A}\left( \nabla \Psi  \right)+{{e}^{2}}{{A}^{2}}\Psi  \right]+V\Psi (\bar{r},t) \\

\end{align}

TeX (checked):

{\begin{aligned}&i\hbar {\dot {\Psi }}({\bar {r}},t)={\frac {1}{2m}}\left({\frac {\hbar }{i}}\nabla -e{\bar {A}}\right)\left({\frac {\hbar }{i}}\nabla -e{\bar {A}}\right)\Psi ({\bar {r}},t)+V\Psi ({\bar {r}},t)\\&={\frac {1}{2m}}\left[-{{\hbar }^{2}}\Delta \Psi +i\hbar e\nabla \left({\bar {A}}\Psi \right)+i\hbar e{\bar {A}}\left(\nabla \Psi \right)+{{e}^{2}}{{A}^{2}}\Psi \right]+V\Psi ({\bar {r}},t)\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (4.022 KB / 558 B) :

\begin{aligned} i ℏ \dot{Ψ} (\bar{r}, t) = \frac{1}{2 m} (\frac{ℏ}{i} \nabla - e \bar{A}) (\frac{ℏ}{i} \nabla - e \bar{A}) Ψ (\bar{r}, t) + V Ψ (\bar{r}, t) \\ = \frac{1}{2 m} [- ℏ^{2} Δ Ψ + i ℏ e \nabla (\bar{A} Ψ) + i ℏ e \bar{A} (\nabla Ψ) + e^{2} A^{2} Ψ] + V Ψ (\bar{r}, t) \end{aligned}

<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">&#x03A8;</mi><mo>˙</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">&#x2207;</mi><mo>&#x2212;</mo><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">&#x210F;</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">&#x2207;</mi><mo>&#x2212;</mo><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mi>V</mi><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mo>&#x2212;</mo><msup><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">&#x0394;</mi><mi mathvariant="normal">&#x03A8;</mi><mo>+</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><mi>e</mi><mi mathvariant="normal">&#x2207;</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">&#x2207;</mi><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mi>V</mi><mi mathvariant="normal">&#x03A8;</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$i$

$\dot{Ψ}$

$\bar{r}$

$t$

$m$

$i$

$e$

$\bar{A}$

$i$

$e$

$\bar{A}$

$Ψ$

$\bar{r}$

$t$

$V$

$Ψ$

$\bar{r}$

$t$

$m$

$Δ$

$Ψ$

$i$

$e$

$\bar{A}$

$Ψ$

$i$

$e$

$\bar{A}$

$Ψ$

$e$

$A$

$Ψ$

$V$

$Ψ$

$\bar{r}$

$t$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search