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[quote="Lisa92"][latex](\delta_{il}*\delta_{kk}-\delta_{ik}*\delta_{km}) B_{k} &=& (\delta_{il}-\delta_{im}) B_{k}[/latex] Nur wie hilft mir das weiter?[/quote]
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<table border="0" cellpadding="3" cellspacing="1" width="100%" class="forumline"> <tr> <th class="thCornerL" width="22%" height="26">Autor</th> <th class="thCornerR">Nachricht</th> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 29. Nov 2011 00:11<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">bitte</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 29. Nov 2011 00:11<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Omg ja danke! jetzt hab ichs endlich verstanden *g* Vielen Dank für die geduldige Hilfe!</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 29. Nov 2011 00:09<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Summenkonvention!!! <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\delta_{ll} = \sum_{l=1}^3 \delta_{ll} = \sum_{l=1}^3 1 = 3"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 29. Nov 2011 00:05<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?( \delta_{im} - \delta_{im}) B_m"> <br />Dann kommt doch 0 raus?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 29. Nov 2011 00:02<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">(sorry, bei mir war der Index am B falsch) <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_i = \frac{1}{2}\, \epsilon_{ikl}\,\epsilon_{lmk}B_m = \frac{1}{2}\, \left( \delta_{ll}\delta_{im} - \delta_{lm} \delta_{li}\right) B_m"> <br /> <br />Und kriegst du jetzt die Summation über l hin?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:56<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?(\delta_{il}*\delta_{kk}-\delta_{ik}*\delta_{km}) B_{k} <br />&=& (\delta_{il}-\delta_{im}) B_{k}"> <br /> <br />Nur wie hilft mir das weiter?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:52<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">So, jetzt kannst du deine Formel für die Summe über die beiden Epsilon-Symbole einsetzen</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:51<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ja, das ist klar</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:50<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_i = \frac{1}{2}\, \epsilon_{ikl}\,\epsilon_{lmn}B_m\,\delta_{kn} = \frac{1}{2}\, \epsilon_{ikl}\,\epsilon_{lmk}B_m"> <br /> <br />Ist der Schritt klar?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:47<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Ok Danke, wie mache ich nun weiter? Ich bekomme ja immer 0 heraus..</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:45<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Zunächst mal einsetzen <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_i = \epsilon_{ikl}\partial_k A_l = \frac{1}{2}\, \epsilon_{ikl}\,\partial_k \,\epsilon_{lmn}B_m x_n = \frac{1}{2}\, \epsilon_{ikl}\,\epsilon_{lmn}B_m\,\partial_k\,x_n "> <br /> <br />Jetzt die Ableitung auswerten: <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_k\,x_n = \delta_{kn}"> <br /> <br />Einsetzen liefert <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_i = \frac{1}{2}\, \epsilon_{ikl}\,\epsilon_{lmn}B_m\,\delta_{kn} "> <br /> <br />Das Ableiten erzeugt die Kronecker-Deltas - und nach dem Ableiten ist die Ableitung weg!</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:32<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_{i}&=&\tfrac{1}{2} \epsilon _{ijk} \partial_{i}\epsilon _{lmj} B_{l} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{ijk} \epsilon _{lmj} B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{kij} \epsilon _{jlm} B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} (\delta_{kl}\delta_{im}-\delta_{km}\delta_{il}) B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} B_{l}\partial_{m} x_{m} - \tfrac{1}{2} B_{l}\partial_{l} x_{m} <br />&=& \tfrac{1}{2} B_{l}- \tfrac{1}{2} B_{l}\delta_{ll}"> <br /> Meinst du das so?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:28<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"></span><table width="90%" cellspacing="1" cellpadding="3" border="0" align="center"><tr> <td><span class="genmed"><b>Lisa92 hat Folgendes geschrieben:</b></span></td> </tr> <tr> <td class="quote">Srry, ich kenne mich mit Latex noch nicht so aus =(</td> </tr></table><span class="postbody"> <br />Sorry, aber das liegt in an LaTeX ;-) <br /> <br />Du kannst bei einer Vektor- bzw. Marixgleichung jeden Index nur einmal (frei) oder zweimal (darüber summiert) haben. <br /> <br />Wenn du <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?x_i"> nach <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?x_k"> ableitest, dann kommt ein <img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\delta_{ik}"> dabei raus; sonst ändert sich nichts. <br /> <br />Wo du plötzlich die doppelten Kronecker-Deltas herbekommst obwohl du noch einen Ableitungsterm dastehen hast, ist mir schleierhaft; ich denke, die Ableitung ist einfach irrigerweise nochmal falsch abgeschrieben, oder?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:21<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_{i}&=&\tfrac{1}{2} \epsilon _{ijk} \partial_{i}\epsilon _{lmj} B_{l} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{ijk} \epsilon _{lmj} B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{kij} \epsilon _{jlm} B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} (\delta_{kl}\delta_{im}-\delta_{km}\delta_{il}) B_{l}\partial_{i} x_{m} <br />&=& \tfrac{1}{2} B_{l}\partial_{m} x_{m} - \tfrac{1}{2} B_{l}\partial_{l} x_{m}"> <br /> <br />Srry, ich kenne mich mit Latex noch nicht so aus =(</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:18<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody">Nein, leider nicht. <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\partial_i x_k = \delta_{ik}"> <br /> <br />Es gibt kein Kronecker-Delta mir nur einem Index.</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:16<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_{i}&=&\tfrac{1}{2} \epsilon _{ijk} \delta_{i}\epsilon _{lmj} B_{l} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{ijk} \epsilon _{lmj} B_{l}\delta_{i} x_{m} <br />&=& \tfrac{1}{2} \epsilon _{kij} \epsilon _{jlm} B_{l}\delta_{i} x_{m} <br />&=& \tfrac{1}{2} (\delta_{kl}\delta_{im}-\delta_{km}\delta_{il}) B_{l}\delta_{i} x_{m} <br />&=& \tfrac{1}{2} B_{l}\delta_{m} x_{m} - \tfrac{1}{2} B_{l}\delta_{l} x_{m}"> <br /> <br />Stimmt das soweit?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row1"><span class="name"><a name=""></a><b>TomS</b></span></td> <td class="row1" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 23:07<span class="gen"> </span> Titel: </span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?B_i = \epsilon_{ikl}\partial_k A_l "> <br /> <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?A_i = \frac{1}{2}\, \epsilon_{ikl}B_k x_l"></span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> <tr> <td width="22%" align="left" valign="top" class="row2"><span class="name"><a name=""></a><b>Lisa92</b></span></td> <td class="row2" height="28" valign="top"><table width="95%" border="0" cellspacing="0" cellpadding="0"> <tr> <td width="95%"><img src="templates/subSilver/images/icon_minipost.gif" width="12" height="9" alt="Beitrag" title="Beitrag" border="0" /><span class="postdetails">Verfasst am: 28. Nov 2011 22:56<span class="gen"> </span> Titel: Vektorpotential im homogenen Magnetfeld</span></td> </tr> <tr> <td colspan="2"><hr /></td> </tr> <tr> <td colspan="2"><span class="postbody"><span style="font-weight: bold">Meine Frage:</span> <br />Hallo, ich soll mithilfe des Epsilon Tensors zeigen, dass für <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec{B} = \operatorname{rot}(\vec{A})"> <br />ein Vektorpotential gegeben ist durch: <br /><img class="latex2png" src="https://www.matheboard.de/latex2png/latex2png.php?\vec{A} = \tfrac{1}{2} \cdot \vec{B} \times \vec{x}"> <br />Lg Lisa <br /> <br /><span style="font-weight: bold">Meine Ideen:</span> <br />Ich schreibe B und A mithilfe des Epsilon Tensors, dann setze ich den Ausdruck für A in den von B ein und komme letztlich auf 0.... Weiß vllt jemand nen Link wo das vllt durchgerechnet wird?</span></td> </tr> </table></td> </tr> <tr> <td colspan="2" height="1" class="spaceRow"><img src="templates/subSilver/images/spacer.gif" alt="" width="1" height="1" /></td> </tr> </table>
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