Timeline for Difficulty with the usage of Cauchy's integral formula in Griffiths QM book
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17 events
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| Aug 19, 2014 at 21:29 | history | edited | kalkanistovinko |
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| Aug 19, 2014 at 21:25 | answer | added | Robin Ekman | timeline score: 6 | |
| Aug 19, 2014 at 20:55 | comment | added | Qmechanic♦ | Hi kalkanistovinko. If you haven't already done so, please take a minute to read the definition of when to use the homework tag, and the Phys.SE policy for homework-like problems. | |
| Aug 19, 2014 at 20:53 | comment | added | JeffDror | The point is that if you choose a contour to not include the poles in the "half semi circle way" then the real integral isn't actually equal to the complex integral. The two integrals being equal hinges on the fact that the half-semi circle needs to be zero. This is known as Jordan's lemma. | |
| Aug 19, 2014 at 20:45 | comment | added | webb | The usual trick is to shift the poles off the real axis then take the limit of the pole moving back onto the axis. If you do the contour integration correctly, the answer is unique. | |
| Aug 19, 2014 at 19:59 | history | edited | kalkanistovinko |
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| Aug 19, 2014 at 19:58 | history | edited | Qmechanic♦ | CC BY-SA 3.0 |
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| Aug 19, 2014 at 19:21 | history | edited | kalkanistovinko | CC BY-SA 3.0 |
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| Aug 19, 2014 at 19:07 | comment | added | kalkanistovinko | I assure you, too, that I'm by NO means questioning the rigor of contour integration, but the way it's applied to my specific case. | |
| Aug 19, 2014 at 19:04 | comment | added | Danu | I assure you, contour integration is perfectly rigorous (although I didnt inspect your specific case). | |
| Aug 19, 2014 at 18:52 | comment | added | kalkanistovinko | The reason why I'm questioning the rigor is that the real integral can have no more than one value, while different choices of the contours yield different answers. | |
| Aug 19, 2014 at 18:49 | comment | added | kalkanistovinko | @Phonon The reason why your link doesn't resolve the issue is that, in my case, the poles are right in the original real integral interval | |
| Aug 19, 2014 at 18:41 | comment | added | Ellie | Look for "Residue theorem" en.wikipedia.org/wiki/Residue_theorem , there are plenty of lectures on it available on youtube as well. | |
| Aug 19, 2014 at 18:40 | comment | added | Danu | Then read up on it. An elementary approach is outlined in e.g. Kreyszig's book 'Advanced Engineering Mathematics' | |
| Aug 19, 2014 at 18:39 | comment | added | kalkanistovinko | That's the fundamental problem actually: I haven't! | |
| Aug 19, 2014 at 18:38 | comment | added | Danu | Have you ever taken a course on complex analysis? I suggest you read up a little on that topic; this seems to be a standard application. | |
| Aug 19, 2014 at 18:37 | history | asked | kalkanistovinko | CC BY-SA 3.0 |