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Display information for equation id:math.2706.143 on revision:2706

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2706.143)

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Hash: 1272821636677e2ef26bdf769fafd060

TeX (original user input):

\begin{align}
& \mathfrak{i} {{\partial }_{t}}\left| \chi \left( t \right) \right\rangle =\hat{H}\left( t \right)\left| \chi \left( t \right) \right\rangle  \\
& \Leftrightarrow \begin{matrix}
\begin{align}
& \mathfrak{i} {{{\dot{\chi }}}_{1}}={{B}_{z}}{{\chi }_{1}}-B_{||}^{*}{{\chi }_{2}} \\
& \mathfrak{i} {{{\dot{\chi }}}_{2}}=B_{||}^{{}}{{\chi }_{1}}-{{B}_{z}}{{\chi }_{2}} \\
\end{align} & {}  \\
\end{matrix} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\mathfrak {i}}{{\partial }_{t}}\left|\chi \left(t\right)\right\rangle ={\hat {H}}\left(t\right)\left|\chi \left(t\right)\right\rangle \\&\Leftrightarrow {\begin{matrix}{\begin{aligned}&{\mathfrak {i}}{{\dot {\chi }}_{1}}={{B}_{z}}{{\chi }_{1}}-B_{||}^{*}{{\chi }_{2}}\\&{\mathfrak {i}}{{\dot {\chi }}_{2}}=B_{||}^{}{{\chi }_{1}}-{{B}_{z}}{{\chi }_{2}}\\\end{aligned}}&{}\\\end{matrix}}\\\end{aligned}}

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MathML (2.991 KB / 509 B) :

𝔦t|χ(t)=Ĥ(t)|χ(t)𝔦χ˙1=Bzχ1B||χ2𝔦χ˙2=B||χ1Bzχ2
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mi></mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>χ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE"></mo></mrow><mo stretchy="false">=</mo><mover><mi>H</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>χ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE"></mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false"></mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mover><mi>χ</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">=</mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><msub><mi>χ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false"></mo><msubsup><mi>B</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mo stretchy="false">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0"></mo></mrow></msubsup><msub><mi>χ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><msub><mover><mi>χ</mi><mo>˙</mo></mover><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">=</mo><msubsup><mi>B</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">|</mo><mo stretchy="false">|</mo></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></msubsup><msub><mi>χ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false"></mo><msub><mi>B</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow></msub><msub><mi>χ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mtd><mtd></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Formaler Aufbau der Quantenmechanik page

Identifiers

  • 𝔦
  • t
  • χ
  • t
  • Ĥ
  • t
  • χ
  • t
  • 𝔦
  • χ˙1
  • Bz
  • χ1
  • B
  • χ2
  • 𝔦
  • χ˙2
  • B
  • χ1
  • Bz
  • χ2

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