Recent content by Nikratio

Could you be more specific? What is "the integral of a function over a transformation"? I think I am reasonably familiar with calculus of variations and Noether's theorem, but maybe I should refresh my memory because I don't see how either would help me with my question. Could you give more...

Hi, How does one define symmetry of a system? I believe that a scalar function g(\vec x) is called symmetric under a transformation \vec F(\vec x) if and only if g(\vec x) = g(\vec F(\vec x)) If there is an equivalent criteria for vector functions, I would be inclined to define a...

Linear Programming was exactly the right keyword, thank you so much! I should be able to find my way from here on.

Yeah, you're right. What I want is a constrained solution to the system of linear equations. At the beginning I was thinking that maybe I can construct a matrix A^+ such that \vec b = A^+ . \vec c and \vec b satisfies the constraint. Construction of A^+ would then be a "constrained matrix...

Hello, I need to invert a non-square matrix A under the constraint that the absolute value of each component of the solution is less than some maximum. In other words, I want \vec{b} such that A . \vec b = \vec c and |b_i| < \alpha. Are there any established methods for doing this? My...

Actually that is the original form of the boundary condition. I rewrote it in terms of the spatial derivative so that I could use separation of variables. Did I miss something obvious? To me this form seems even less tractable...

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

Hi, For some reason I always believed that I can generally exchange the order of integration for multiple integrals, i.e. \int \int f(x,y) \; dx \; dy = \int \int f(x,y) \; dy \; dx However, I just had to realize that this cannot be true, since (with a a constant): \int \int \frac{d...

Hello, Is there a general, analytic way to obtain a vector potential for a prescribed magnetic field? I.e. to solve \vec \nabla \times \vec A = \vec B for \vec A? I'm looking for something like what e.g. the Green's function method is for Poisson's equation, so the answer might be a...

Yes, that was it! Thank you very much!

Hello, In order to test-drive a data analysis program, I am looking for a function that generates sine waves with slowly oscillating frequency, i.e. the distance between the maxima should be slowly changing. I thought that I could simply achieve this by using a function of the form f(t)...

Yes, that's what I expected. But is there a common way to distinguish between these two states? I could probably construct an observable that commutes with S^2 and S_z and distinguishes between these states, but I'd like to know whether there is a standard way of choosing this observable.

Hello, I am considering the case of the total spin when adding three spin 1/2s. The combined system has dimension 2x2x2=8. The possible values for the total spin quantum number are: \left([1/2] \otimes [1/2]) \otimes [1/2] = ([1] \oplus [0]) \otimes [1/2] =[3/2] \oplus [1/2] \oplus [1/2]...