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

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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. --KSmrq^T 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)

???

8976876876876^0.1

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.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)