- testwiki

General

Display information for equation id:math.1726.13 on revision:1726

* Page found: Zeitabhängige Störungsrechnung (eq math.1726.13)

Occurrences on the following pages:

Zeitabhängige Störungsrechnung Eq: math.1732.13

Hash: b5946435815715ea3ae01232c95d7f11

TeX (original user input):

\begin{align}

& \hat{H}{{\left| \Psi  \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| \Psi  \right\rangle }_{t}} \\

& \Rightarrow \sum\limits_{n}{{}}{{c}_{n}}(t)\hat{H}\left| n \right\rangle =i\hbar \sum\limits_{n}{{}}\frac{d}{dt}{{c}_{n}}(t)\left| n \right\rangle =\sum\limits_{n}{{}}{{c}_{n}}(t)\left( {{{\hat{H}}}_{0}}+{{{\hat{H}}}^{1}}(t) \right)\left| n \right\rangle =\sum\limits_{n}{{}}{{c}_{n}}(t)\left( {{E}_{n}}+{{{\hat{H}}}^{1}}(t) \right)\left| n \right\rangle  \\

\end{align}

TeX (checked):

{\begin{aligned}&{\hat {H}}{{\left|\Psi \right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi \right\rangle }_{t}}\\&\Rightarrow \sum \limits _{n}{}{{c}_{n}}(t){\hat {H}}\left|n\right\rangle =i\hbar \sum \limits _{n}{}{\frac {d}{dt}}{{c}_{n}}(t)\left|n\right\rangle =\sum \limits _{n}{}{{c}_{n}}(t)\left({{\hat {H}}_{0}}+{{\hat {H}}^{1}}(t)\right)\left|n\right\rangle =\sum \limits _{n}{}{{c}_{n}}(t)\left({{E}_{n}}+{{\hat {H}}^{1}}(t)\right)\left|n\right\rangle \\\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 (4.023 KB / 556 B) :

\begin{aligned} \hat{H} {| Ψ ⟩}_{t} = i ℏ \frac{\partial}{\partial t} {| Ψ ⟩}_{t} \\ \Rightarrow \sum_{n} c_{n} (t) \hat{H} | n ⟩ = i ℏ \sum_{n} \frac{d}{d t} c_{n} (t) | n ⟩ = \sum_{n} c_{n} (t) ({\hat{H}}_{0} + {\hat{H}}^{1} (t)) | n ⟩ = \sum_{n} c_{n} (t) (E_{n} + {\hat{H}}^{1} (t)) | n ⟩ \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><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo>=</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>t</mi></mrow></mrow></mfrac></mrow><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">&#x03A8;</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>d</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow></mfrac></mrow><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>+</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow><mo>=</mo><munder><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munder><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo>+</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>H</mi><mo>^</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">&#x27E9;</mo></mrow></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

$\hat{H}$

$Ψ_{t}$

$i$

$t$

$Ψ_{t}$

$n$

$c_{n}$

$t$

$\hat{H}$

$n$

$i$

$n$

$d$

$d$

$t$

$c_{n}$

$t$

$n$

$n$

$c_{n}$

$t$

${\hat{H}}_{0}$

$\hat{H}$

$t$

$n$

$n$

$c_{n}$

$t$

$E_{n}$

$\hat{H}$

$t$

$n$

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