# Recent content by bndnchrs

1. ### Rational Dependence

Much appreciated. I believe this solves my question. Don't worry about revealing the "proof", I would say that this problem is just a redefinition of a small mechanism in a larger problem, which has nothing to do with linear algebra, actually, so letting me in on the mechanism is of no great...
2. ### Rational Dependence

I suppose it was late, and this meant I had to improperly state the question! Really, the question is does the set of RD vectors have nonzero measure over R^k, not whether they are dense or not. Of course the rationals are rationally dependent and dense, but they are a set of measure zero in R...
3. ### Rational Dependence

Hi guys: I've got a problem I've been working on for some weeks and this might be the key to unlocking it. The question is: Given a vector in R^k, what is the measure of the set of vectors whose components are rationally dependent? Rationally dependent means for a given vector, you may...
4. ### Variation of simple Lagrangian

Hey, I'm doing some examples in QFT and I don't want to go too far with this one: Doing gauge symmetries, we first introduce the Unitary spacetime-dependent gauge transformation that gives us a gauge potential. With the new gauge added Lagrangian, I want to take its variation to confirm the...
5. ### Mean value of a harmonic function on a square

Homework Statement The idea is to prove that the average of a harmonic function over a square is the same as the average over its diagonals. Homework Equations Really, none, other than the mean value theorem, that is the value of the function at a point is the same as the average of...
6. ### Valid Estimation of Square Roots?

right, just approximating x by floors and ceilings
7. ### Valid Estimation of Square Roots?

Right: I just meant the ratio, not the relative error. I just did \frac{yours}{actual} I don't understand that third statement: the largest error in [m,n] is at m + sqrt(m)? This isn't always in the interval. I'm also not sure what you mean by 2) your largest error is at two points? The error...
8. ### An intuitive explanation to the Killing equation?

I think the easiest way to explain it is by what Wikipedia has: A Killing field is one where when you move points along the field, distances are preserved. So http://en.wikipedia.org/wiki/Killing_vector_field" [Broken] when you'e got a Killing field.
9. ### Valid Estimation of Square Roots?

This is like a weight combo of up and down Bahkshali, right? Here's your relative error: It has an exponential approach curve I think its a smart idea but computationally its as efficient as Bahkshali... and there are more efficient methods than Bahkshali. Mathematica isn't cooperating...
10. ### Perturbation theory / harmonic oscillator

Hi notist, If you are able to write down the perturbed Hamiltonian, you should be able to run through these computations quite easily :). The idea is that to first order perturbation, the energy shifts are essentially the same as the expectation value of the perturbing Hamiltonian. It...
11. ### Boundary Value Problem for the 1-D Wave

should be moved to homework... sorry!
12. ### Boundary Value Problem for the 1-D Wave

So here's the problem: I'm asked to find the solutions to the 1-D Wave equation u_{tt} = u_{xx} subject to u(x,0) = g(x), u_t(x,0) = h(x) but also u_t(0,t) = A*u_x(0,t) and discuss why A = -1 does not allow valid solutions. I can't figure it out at all. The solutions to...
13. ### Help with first integral of PDE

right... the problem is this solution isn't as easy as all that... there is a more trivial example solved with \frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{z(x+y)} Which can be solved by doing some proper addition and subtraction: so I know the idea. Its a matter of getting a form \frac{g*dx...
14. ### Help with first integral of PDE

Hey guys, I'm having a little difficulty with a pde I'm trying to solve. It boils down to solving for a first integral. I don't want the answer, but I'd be glad to get a little help. We have the system: \frac{dx}{x^2} = \frac{dy}{y^2} = \frac{dz}{xy(z^2 + 1)} We can use the first two and find...
15. ### PDE: The Eikonal Equation method of characterstics, etc.

Homework Statement I need to solve the Eikonal Equation c^2(u_x^2 + u_y^2) = 1 Initial condition u(x,0) = 0 C(x,y) = |x|, but x>0 to essentially C = x Oh. And the solution is given as \ln{\frac{\sqrt{x^2 + y^2} + y}{x}} Homework Equations None other than the usual method of...