Wikipedia:Reference desk/Archives/Mathematics/2007 February 12
From Wikipedia, the free encyclopedia
| Mathematics desk | ||
|---|---|---|
| < February 11 | << Jan | February | Mar >> | February 13 > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
|---|
| The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Contents |
[edit] February 12
[edit] Mathematical basis of quantum physics
Quantum physics (as I understand it, at least), is dependent upon a number of results in complex analysis and linear algebra. Does anyone know what properties of the underlying "number system" (pardon my vernacular) 
(the complex numbers) are essential to the development of these results, and thus quantum physics? I speak of things like the fact that is algebraically closed (though that may not, in fact, be relevant - it just illustrates what I mean when I say "properties"). --Braveorca 05:01, 12 February 2007 (UTC)
- Your question suggests the mathematics shapes the physics; actually, it's the other way around. The result of the two slit experiment is a physical fact, as is the photoelectric effect, as is quantum tunneling, and so on. It is ironic that you ask specifically about quantum mechanics, because its mathematics has a remarkable history. The physical phenomena were originally formalized in completely different ways, which later were shown to be equivalent. --KSmrqT 07:56, 12 February 2007 (UTC)
- Here's one take (scroll down to "Real vs. Complex Numbers"). Fredrik Johansson 12:07, 12 February 2007 (UTC)
[edit] How do you call 1/(1-x)?
How do you call 1/(1-x) or 1 + x + x^2 + x^3 + ...?Mr.K. (talk) 18:02, 12 February 2007 (UTC)
- I don't think there is a very specific name.
is an example of a rational function, and 
(which amounts to the same value for | x | < 1) is an example of a power series. -- Meni Rosenfeld (talk) 18:15, 12 February 2007 (UTC)
-
- I think the better link for the infinite series is geometric progression. —David Eppstein 21:52, 12 February 2007 (UTC)
-
-
- Through other sources I found that the whole thing may be called: "Gram-Schmidt Identity". Although there is a wikipedia article about Gram-Schmidt process, I didn't find more information about the identity (either here, nor somewhere else).Mr.K. (talk) 15:38, 13 February 2007 (UTC)
-
[edit] ???
89768768768760.1
- 8976876876876^0.1 = 19.7384264 --Spoon! 21:50, 12 February 2007 (UTC)
[edit] Frequency of occurrence
Using a TI-83 Plus, is it possible to calculate (or count) the number of occurrences of an element in a list without using an third-party application or graphing? I.e., if I have {1, 1, 2, 3, 3, 3} stored to List 1 (L1), can I have the calculator count the number of times the number "3" appears? Thanks. --MZMcBride 22:40, 12 February 2007 (UTC)
- If it's in a program, best way I can think of is a subroutine, comparing each element and incrementing a counter value.ST47Talk 00:21, 13 February 2007 (UTC)
- Using C as the counter, E as the element input, L as the loop variable, and your L1:
PROGRAM:LSTCOUNT :0→C :Input "ELEMENT? ",E :For(L,1,dim(L1)) :If L1(L)=E:Then :C+1→C:End:End :Disp "FREQUENCY:",C
- Running the program:
prgmLSTCOUNT
ELEMENT? 3
FREQUENCY:
3
Done
- The dim( function is in the LIST OPS menu. --jh51681 13:02, 16 February 2007 (UTC)
