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* Page found: Master Gleichung (eq 27) (force rerendering)

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   Master Gleichung Eq: 27
TeX (as stored in database):
\begin{align}
  & {{d}_{t}}\tilde{\rho }=-\mathfrak{i}\left[ {{{\tilde{H}}}_{I}},{{\rho }_{0}}-\mathfrak{i}\int_{0}^{t}{[{{{\tilde{H}}}_{I}},\tilde{\rho }]}\,d{t}' \right] \\
 & =-\mathfrak{i}\left[ {{{\tilde{H}}}_{I}},{{\rho }_{0}} \right]-\left[ {{{\tilde{H}}}_{I}},\int_{0}^{t}{[{{{\tilde{H}}}_{I}},\tilde{\rho }]}\,d{t}' \right] \\
 & =-\mathfrak{i}\left[ {{{\tilde{H}}}_{I}},{{\rho }_{0}} \right]-\int_{0}^{t}{\left[ {{{\tilde{H}}}_{I}},\left[ {{{\tilde{H}}}_{I}},\,\tilde{\rho } \right] \right]}d{t}'
\end{align}
MathML (27.93 KB / 3.381 KB) :
dtρ~=-𝔦[H~I,ρ0-𝔦0t[H~I,ρ~]dt]subscriptdtnormal-~ρ𝔦subscriptnormal-~HIsubscriptρ0𝔦superscriptsubscript0tsubscriptnormal-~HInormal-~ρdsuperscripttnormal-′\displaystyle{{d}_{{t}}}\tilde{\rho}=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},% {{\rho}_{{0}}}-\mathfrak{i}\int_{{0}}^{{t}}{[{{{\tilde{H}}}_{{I}}},\tilde{\rho% }]}\,d{t}^{{\prime}}\right]
=-𝔦[H~I,ρ0]-[H~I,0t[H~I,ρ~]dt]absent𝔦subscriptnormal-~HIsubscriptρ0subscriptnormal-~HIsuperscriptsubscript0tsubscriptnormal-~HInormal-~ρdsuperscripttnormal-′\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-% \left[{{{\tilde{H}}}_{{I}}},\int_{{0}}^{{t}}{[{{{\tilde{H}}}_{{I}}},\tilde{% \rho}]}\,d{t}^{{\prime}}\right]
=-𝔦[H~I,ρ0]-0t[H~I,[H~I,ρ~]]dtabsent𝔦subscriptnormal-~HIsubscriptρ0superscriptsubscript0tsubscriptnormal-~HIsubscriptnormal-~HInormal-~ρdsuperscripttnormal-′\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-% \int_{{0}}^{{t}}{\left[{{{\tilde{H}}}_{{I}}},\left[{{{\tilde{H}}}_{{I}}},\,% \tilde{\rho}\right]\right]}d{t}^{{\prime}}

SVG (0 B / 8 B) :
PNG (0 B / 8 B) :
Hash : 1bc89cb12d7e9cd58db2779e0b46b502

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Variables

15 results

  • mi 𝔦 (4/24/160)
  • mo (3/9/497)
  • mo ~ (12/38/722)
  • mo [ (8/27/1298)
  • mo ] (8/27/1300)
  • mi ρ (7/49/1711)
  • mo (3/6/2089)
  • mi H (8/60/2732)
  • mi d (4/13/6342)
  • mi I (8/40/7943)
  • mo , (8/33/8858)
  • mi t (7/27/10589)
  • mo - (6/23/10795)
  • mo = (3/36/18270)
  • mo (11/85/59187)

MathML


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xml:id="S0.Ex1.m2.1.29.2.1.2.3.2.2.2.3.cmml" xref="S0.Ex1.m2.1.29.2.1.2.3.2.2.2.3"><csymbol cd="ambiguous" xml:id="S0.Ex1.m2.1.29.2.1.2.3.2.2.2.3.1.cmml">superscript</csymbol><ci xml:id="S0.Ex1.m2.1.26.cmml" xref="S0.Ex1.m2.1.26">t</ci><ci xml:id="S0.Ex1.m2.1.27.1.cmml" xref="S0.Ex1.m2.1.27.1">normal-′</ci></apply></apply></apply></apply></apply></apply></apply></apply></apply></annotation-xml><annotation xml:id="S0.Ex1.m2.1b" encoding="application/x-tex" xref="S0.Ex1.m2.1.cmml">\displaystyle{{d}_{{t}}}\tilde{\rho}=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},%
{{\rho}_{{0}}}-\mathfrak{i}\int_{{0}}^{{t}}{[{{{\tilde{H}}}_{{I}}},\tilde{\rho%
}]}\,d{t}^{{\prime}}\right]</annotation></semantics></math></td>
<td class="ltx_eqn_pad"/></tr>
<tr id="S0.Ex2" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"/>
<td class="ltx_td ltx_align_right"/>
<td class="ltx_td ltx_align_left"><math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex2.m2" class="ltx_Math" alttext="\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-%&#10;\left[{{{\tilde{H}}}_{{I}}},\int_{{0}}^{{t}}{[{{{\tilde{H}}}_{{I}}},\tilde{%&#10;\rho}]}\,d{t}^{{\prime}}\right]" xml:id="S0.Ex2.m2.1" display="inline" xref="S0.Ex2.m2.1.cmml"><semantics xml:id="S0.Ex2.m2.1a" xref="S0.Ex2.m2.1.cmml"><mrow xml:id="S0.Ex2.m2.1.30" xref="S0.Ex2.m2.1.30.cmml"><none xml:id="S0.Ex2.m2.1.30.1" xref="S0.Ex2.m2.1.30.1.cmml"/><mo xml:id="S0.Ex2.m2.1.1" xref="S0.Ex2.m2.1.1.cmml">=</mo><mrow xml:id="S0.Ex2.m2.1.30.2" xref="S0.Ex2.m2.1.30.2.cmml"><mrow xml:id="S0.Ex2.m2.1.30.2.1" xref="S0.Ex2.m2.1.30.2.1.cmml"><mo xml:id="S0.Ex2.m2.1.2" xref="S0.Ex2.m2.1.2.cmml">-</mo><mrow xml:id="S0.Ex2.m2.1.30.2.1.1" xref="S0.Ex2.m2.1.30.2.1.1.cmml"><mi xml:id="S0.Ex2.m2.1.3" xref="S0.Ex2.m2.1.3.cmml">𝔦</mi><mo xml:id="S0.Ex2.m2.1.30.2.1.1.1" 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xml:id="S0.Ex2.m2.1.14.1.cmml" xref="S0.Ex2.m2.1.14.1">I</ci></apply><apply xml:id="S0.Ex2.m2.1.30.2.2.3.cmml" xref="S0.Ex2.m2.1.30.2.2.3"><apply xml:id="S0.Ex2.m2.1.30.2.2.3.1.cmml" xref="S0.Ex2.m2.1.30.2.2.3.1"><csymbol cd="ambiguous" xml:id="S0.Ex2.m2.1.30.2.2.3.1.1.cmml">superscript</csymbol><apply xml:id="S0.Ex2.m2.1.30.2.2.3.1.2.cmml"><csymbol cd="ambiguous" xml:id="S0.Ex2.m2.1.30.2.2.3.1.2.1.cmml">subscript</csymbol><int xml:id="S0.Ex2.m2.1.16.cmml" xref="S0.Ex2.m2.1.16"/><cn type="integer" xml:id="S0.Ex2.m2.1.17.1.cmml" xref="S0.Ex2.m2.1.17.1">0</cn></apply><ci xml:id="S0.Ex2.m2.1.18.1.cmml" xref="S0.Ex2.m2.1.18.1">t</ci></apply><apply xml:id="S0.Ex2.m2.1.30.2.2.3.2.cmml" xref="S0.Ex2.m2.1.30.2.2.3.2"><times xml:id="S0.Ex2.m2.1.30.2.2.3.2.1.cmml" xref="S0.Ex2.m2.1.30.2.2.3.2.1"/><apply xml:id="S0.Ex2.m2.1.30.2.2.3.2.2.cmml" xref="S0.Ex2.m2.1.30.2.2.3.2.2"><interval closure="closed" xml:id="S0.Ex2.m2.1.30.2.2.3.2.2.1.cmml"/><apply xml:id="S0.Ex2.m2.1.30.2.2.3.2.2.2.cmml" xref="S0.Ex2.m2.1.30.2.2.3.2.2.2"><csymbol cd="ambiguous" xml:id="S0.Ex2.m2.1.30.2.2.3.2.2.2.1.cmml">subscript</csymbol><apply xml:id="S0.Ex2.m2.1.20.cmml" xref="S0.Ex2.m2.1.20"><ci xml:id="S0.Ex2.m2.1.20.1.cmml" xref="S0.Ex2.m2.1.20.1">normal-~</ci><ci xml:id="S0.Ex2.m2.1.20.2.cmml" xref="S0.Ex2.m2.1.20.2">H</ci></apply><ci xml:id="S0.Ex2.m2.1.21.1.cmml" xref="S0.Ex2.m2.1.21.1">I</ci></apply><apply xml:id="S0.Ex2.m2.1.23.cmml" xref="S0.Ex2.m2.1.23"><ci xml:id="S0.Ex2.m2.1.23.1.cmml" xref="S0.Ex2.m2.1.23.1">normal-~</ci><ci xml:id="S0.Ex2.m2.1.23.2.cmml" xref="S0.Ex2.m2.1.23.2">ρ</ci></apply></apply><ci xml:id="S0.Ex2.m2.1.26.cmml" xref="S0.Ex2.m2.1.26">d</ci><apply xml:id="S0.Ex2.m2.1.30.2.2.3.2.3.cmml" xref="S0.Ex2.m2.1.30.2.2.3.2.3"><csymbol cd="ambiguous" xml:id="S0.Ex2.m2.1.30.2.2.3.2.3.1.cmml">superscript</csymbol><ci xml:id="S0.Ex2.m2.1.27.cmml" xref="S0.Ex2.m2.1.27">t</ci><ci xml:id="S0.Ex2.m2.1.28.1.cmml" xref="S0.Ex2.m2.1.28.1">normal-′</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation xml:id="S0.Ex2.m2.1b" encoding="application/x-tex" xref="S0.Ex2.m2.1.cmml">\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-%
\left[{{{\tilde{H}}}_{{I}}},\int_{{0}}^{{t}}{[{{{\tilde{H}}}_{{I}}},\tilde{%
\rho}]}\,d{t}^{{\prime}}\right]</annotation></semantics></math></td>
<td class="ltx_eqn_pad"/></tr>
<tr id="S0.Ex3" class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"/>
<td class="ltx_td ltx_align_right"/>
<td class="ltx_td ltx_align_left"><math xmlns="http://www.w3.org/1998/Math/MathML" id="S0.Ex3.m2" class="ltx_Math" alttext="\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-%&#10;\int_{{0}}^{{t}}{\left[{{{\tilde{H}}}_{{I}}},\left[{{{\tilde{H}}}_{{I}}},\,%&#10;\tilde{\rho}\right]\right]}d{t}^{{\prime}}" xml:id="S0.Ex3.m2.1" display="inline" xref="S0.Ex3.m2.1.cmml"><semantics xml:id="S0.Ex3.m2.1a" xref="S0.Ex3.m2.1.cmml"><mrow xml:id="S0.Ex3.m2.1.30" xref="S0.Ex3.m2.1.30.cmml"><none xml:id="S0.Ex3.m2.1.30.1" xref="S0.Ex3.m2.1.30.1.cmml"/><mo xml:id="S0.Ex3.m2.1.1" xref="S0.Ex3.m2.1.1.cmml">=</mo><mrow xml:id="S0.Ex3.m2.1.30.2" xref="S0.Ex3.m2.1.30.2.cmml"><mrow xml:id="S0.Ex3.m2.1.30.2.1" xref="S0.Ex3.m2.1.30.2.1.cmml"><mo xml:id="S0.Ex3.m2.1.2" xref="S0.Ex3.m2.1.2.cmml">-</mo><mrow xml:id="S0.Ex3.m2.1.30.2.1.1" xref="S0.Ex3.m2.1.30.2.1.1.cmml"><mi xml:id="S0.Ex3.m2.1.3" xref="S0.Ex3.m2.1.3.cmml">𝔦</mi><mo xml:id="S0.Ex3.m2.1.30.2.1.1.1" 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xml:id="S0.Ex3.m2.1.29.1.cmml" xref="S0.Ex3.m2.1.29.1">normal-′</ci></apply></apply></apply></apply></apply></annotation-xml><annotation xml:id="S0.Ex3.m2.1b" encoding="application/x-tex" xref="S0.Ex3.m2.1.cmml">\displaystyle=-\mathfrak{i}\left[{{{\tilde{H}}}_{{I}}},{{\rho}_{{0}}}\right]-%
\int_{{0}}^{{t}}{\left[{{{\tilde{H}}}_{{I}}},\left[{{{\tilde{H}}}_{{I}}},\,%
\tilde{\rho}\right]\right]}d{t}^{{\prime}}</annotation></semantics></math></td>
<td class="ltx_eqn_pad"/></tr>
</table>