Hilbert space applications?

[ex-xian]

Hi all. I heard about the site the the Sec Web. Anyway, I'm a math major with philosophy and physics minors, and I'm going to grad school in math this fall.

I'm doing my senior seminar on l2, the set of square summable sequences. I'd like to close my paper and my talk on some applications, but I can't find anything. I know that L2 has some apps for QM, but is there anything you can do with l2? Anything with QM, general physics, or numerical analysis?
Thanks in advance.

[HallsofIvy]

Not really. The main application of l2as well as general ln is as simpler sources of examples having the properites of Ln

[ex-xian]

Originally posted by HallsofIvy
Not really. The main application of l2as well as general ln is as simpler sources of examples having the properites of Ln
So there's nothing you can do with l2? Don't get me wrong, I'm enough a (potential) pure mathematician to appreciate the elegance of l2 absent any applications, but it's be nice to have something.



ps,
Is there a list of code for the math symbols.

[Dimitri Terryn]

Not in the strictest sence, no, but since every seperable Hilbert space is isomorfic to l², if you study this little guy you've studied them all, as my analysis professor so nicely said.

And since separable Hilbert-spaces are important in physics (like the aformentioned L²), it does have a use since some properties might be easier studied in l².