Recent content by Skatch

Tha\eta ks!

trans: Won't quite work for my application, I need M to be independant of the matrix I want to apply it to. I'm going to be applying it many times, so I don't want to be computing an new inverse each iteration. Ray: I think you nailed it. After you said I would need to use n^2 by n^2 and...

micromass: Nope, both nxn matrices. u is an approximate solution over a grid of nxn points, u_ij = u(x_i, y_j). I just might be headed down a dead end, and might need to define a different L for my discrete laplacian so that I can invert it. This current setup looks like it probably won't work.

Yeah, u and L definitely don't commute in this case unfortunately. L is a finite difference operator, and how I've got it set up, it gives me the 2nd derivative approximations for u with respect to x when multiplied on the left, and with respect to y when multiplied on the right. So Lu+uL is...

This isn't really a homework question, but there are more people in this forum, hopefully someone can help. Just basic linear algebra. I've got this operator in the form of a matrix, L. It acts on another matrix, u, either by multiplying on the left or right. The operation I want in this...

I've got something like u + LuL^T = v and I want to write it like u = B_1 v B_2 for some B_1 and B_2. Assume L is nice and invertible. Is this impossible or am I just not seeing it? This is making me feel dumb. Too much programming and its getting late.

Can someone tell me if the following statement is true? Say you have P(x)e^{Q(x)} where P(x) is any finite-degree polynomial and Q(x) is a polynomial of integer order k. Is it true that for any positive epsilon, I can find some real numbers A and B such that |P(x)e^{Q(x)}| \leq...

Kanato, thanks for taking the time to reply, that helps a lot. I had to read it a couple times but I think I see now where I was going wrong. "Coherance" was something we covered right at the end of my QM course, and I didn't quite get it at the time, but your last paragraph here helps a lot...

So, I'm doing some undergraduate research in quantum spin systems, looking at the ground states of the Heisenberg Hamiltonian, H=\sum{J_{ij}\textbf{S}_{i}\textbf{S}_{j}}. But I think I have a critical misunderstanding of some fundamental quantum mechanics concepts. (I'm a math major, only had...

Okay, so I think I've come to the conclusion that the Parity of the antiproton is -1. I read that, in general, P(fermion * antifermion) = -1, and since proton's parity is +1, I'm going to conclude that parity of the antiproton is -1. Okay, so total parity on the left hand side of the...

Homework Statement A proton and antiproton at rest in an S-state annihilate to produce \pi0\pi0 pairs. Show that this reaction cannot be a strong interaction. Homework Equations I interpret this problem as: p + p_bar -> \pi0 + \pi0 The Attempt at a Solution If this were a strong...

The hints were leaning toward letting f(x) = (x^2) * sin(x), I think. Not sure how to prove it's a surjection though. Any element, b, of the codomain is certainly mapped to, in fact its mapped to an infinite number of times. But the equation b = x^2 * sin(x) can't be solved explicitly for x. Or...

If E is 5cm, then Sqrt[x^2+y^2] must equal 5cm. And if its parallel to F, it must have the same angle with respect to x-hat, that is ArcTan[y/x] must equal ArcTan[-7/6], which implies -7x = 6y. Two equations and two unknowns. You'll get two possible vectors, one parallel and one anti-parallel.

mrjoe, your substitution method is by no means rigorous. In simple cases, it can give you the correct answer, but the limit of this problem is definitely not 1. The original poster was correct to change it to a power of e, then study the limit of the exponent. You get e raised to the power...

So, if I set F equal to what I stated above, I get an answer of: \int( F \cdot V ) dt = \int(16384 a t^2 - 2048 a t^3 + 256 a t^4)dt = (4063232 a)/15 I don't even know what to make of that...