Wikipedia:Reference desk/Archives/Mathematics/2007 February 12

= February 12 =

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) $$\mathbb{C}$$ (the complex numbers) are essential to the development of these results, and thus quantum physics? I speak of things like the fact that $$\mathbb{C}$$ 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)

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. $$\frac{1}{1-x}$$ is an example of a rational function, and $$1+x+x^2+x^3+\cdots$$ (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)

???
89768768768760.1
 * 8976876876876^0.1 = 19.7384264 --Spoon! 21:50, 12 February 2007 (UTC)

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.ST47 Talk 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)