Timeline for Functional Analysis and its relation to mechanics
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2011 at 9:51 | vote | accept | user7223 | ||
| Jul 1, 2010 at 17:07 | answer | added | Nate Eldredge | timeline score: 1 | |
| Jul 1, 2010 at 10:25 | comment | added | Willie Wong | @Yemon: I am going to channel a physicist acquaintance of mine to illustrate why I don't really consider the sort of stuff in basic ODE theory functional analysis (though you are absolutely right that there is a an application of functional analysis). He said, during a (physics) seminar, to the nodding approval of the (physics) big wigs in the room: "... and as we all know, ODEs good; PDEs bad." | |
| Jul 1, 2010 at 9:55 | answer | added | Helge | timeline score: 5 | |
| Jul 1, 2010 at 9:39 | comment | added | Helge | @Yemon: The proof of Picard-Lindeloef (and cousins) is a functional analysis proof, since it's a fixed point theorem in Banach spaces. It still doesn't give the theory a functional analytic flavour. The key problem is that the functions, one considers do not live in nice spaces. (Exceptions are known. e.g. Sturm--Liouville Theory, but that is more quantum mechanics). | |
| Jul 1, 2010 at 4:48 | answer | added | Tommi | timeline score: 1 | |
| Jul 1, 2010 at 3:21 | comment | added | Yemon Choi | @Willie: I'm very much a non-applications kind of analyst, but doesn't very basic linear ODE theory have a tinge of functional analysis -- at least in early attempts to get somewhere? | |
| Jul 1, 2010 at 1:27 | comment | added | Willie Wong | @Yemon: Only if you are sure there is a connection between classical mechanics and functional analysis. The connections I can think of all require really stretching what falls in the realm of classical mechanics. | |
| Jul 1, 2010 at 0:59 | comment | added | Yemon Choi | Would it be worth splitting this into two questions: one looking at classical mechanics and one at quantum mechanics? | |
| Jul 1, 2010 at 0:42 | comment | added | Willie Wong | Atoms? I somehow associated volume 4 more with semi-conductors, which is most definitely quantum physics. (See Anderson localisation and all that; though of course much of the development in that direction is too recent to have been included in R&S.) But I suppose Fermi's golden rule and friends are really most applicable to atomic ground states. | |
| Jul 1, 2010 at 0:38 | answer | added | Willie Wong | timeline score: 5 | |
| Jul 1, 2010 at 0:23 | answer | added | Eric O. Korman | timeline score: 2 | |
| Jul 1, 2010 at 0:22 | comment | added | Helge | Not to forget Reed-Simon 4, which studies low lying spectra. Meaning: Atoms! (Of course one might argue that this is chemistry). | |
| Jul 1, 2010 at 0:22 | answer | added | The Mathemagician | timeline score: 2 | |
| Jul 1, 2010 at 0:18 | comment | added | Willie Wong | Also, let me just warn you that your question may be closed due to its extremely vague nature ("Is there a connection..." questions are often frowned upon here) and as Leandro said, the fact that its answer is available on Wikipedia. Read the "How to Ask" link on the top right corner of the page, and try to edit your question into a more targeted form. | |
| Jul 1, 2010 at 0:13 | comment | added | Willie Wong | Also see Reed and Simon, Methods of Modern Mathematical Physics, vols 1 - 4. One might argue that the entire tome (well, maybe less so the first half of volume 2 and parts of volume 3) is about application of functional analysis as inspired by the study of Schrodinger equation. | |
| Jul 1, 2010 at 0:13 | history | edited | Gerry Myerson | CC BY-SA 2.5 |
corrected spelling
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| Jul 1, 2010 at 0:07 | comment | added | Leandro | The answer for your questions is Yes. In particular, for Quantum Mechanics, see von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Anyway you can find also more information and reference, about this relations in wikipedia. | |
| Jun 30, 2010 at 23:52 | history | asked | user7223 | CC BY-SA 2.5 |