Hey astrorob, I would like to make some general remarks regarding your original post here. I say general, as I don't really have any detailed knowledge of the MOND theory.
First off, any new scientific models proposed are rarely accepted immediately without thorough scrutiny. That would, I...
Approximation of the FE feat. "loose notation"
I'm looking for a (professional) relativist to help me clarify something. I refer to the article General Relativity Resolves Galactic Rotation Without Exotic Dark Matter by Cooperstock and Tieu, available here...
My apologies for being so slow to reply. The original article where I read it can be found here: http://arxiv.org/abs/astro-ph/0507619v1
On page 6 (Eq. (11)) is the first equation, and on the following page it is re-expressed as Laplace's equation of some other function \Phi, which the...
Sorry, this is not intentionally related to anything you've written. It is, however, one of the equations that arises from studying an axisymmetric rotating object in gtr, using cylindrical coordinates. The first equation in my OP is one of the components of the Einstein tensor. It is then...
Indeed it is, but the function g as I wrote explicitly, depends only on (r,z). Consider equations (98)-(99) here: http://mathworld.wolfram.com/CylindricalCoordinates.html
\nabla^2 f = \frac{\partial^2 f}{\partial r^2}+\frac{1}{r}\frac{\partial f}{\partial r} + \frac{1}{r^2}\frac{\partial^2...
This problem may be very easy or very difficult (probably the first), but I can't seem to make sense of it, and that annoys me. It's not all that important (at least not yet), but I just can't seem to let it go. Anyways, here it is.
Consider the following PDE:
\frac{\partial^2 f}{\partial...
First off, I've corrected the first equation, now it hopefully makes more sense :smile:
Second, I'm afraid it didn't help me much, the rest of your post. You see, this is really a quantum mechanical course, so I'm a bit surprised we got a problem like this. Anyway, I don't know how to find...
We have a particle with electric charge e that moves in a strong magnetic field B. The particle is constrained to the (x,y)-plane, and the magnetic field is orthogonal to the plane, and constant with B as the z-component of \mathbf{B}.
Furthermore we have the rotationally symmetric form of the...
Of course! Since \sigma_z is diagonal, when it's the exponential, you just get a the same matrix with each diagonal element exponentiated!
Now I finally got an expression for the time dependent vector! It remains, however, to be seen if it's the correct expression.
Anyway, thanks for...
We have a spin state described by a time-dependent density matrix
\rho(t) = \frac{1}{2}\left(\mathbf{1}+\mathbf{r}(t)\cdot \mathbf{\sigma} \right)
Initial condition for the motion is \mathbf{r} = \mathbf{r}_0 at t = 0. We are then asked to give a general expression for \rho(t) in terms of...
Hi, thank you so much for your insight Mr. Jones. I can imagine it wasn't very easy to help when I have such general questions, but I must say, your tips were a very good start.
Now I'll need to take a look at the examples and exercises again with this in mind, but have no fear, I'll probably...
Hi, I need some help understanding basic tensor algebra, especially differentiation. The subject I'm studying is quantum field theory, so I'll use examples from there.
First let's start with a real scalar field. This has a Lagrangian density given by
\mathcal{L} =...
Here's the problem. For a neutral vector field V_{\mu} we have the Lagrangian density
\mathcal{L} = -\frac{1}{2}(\partial_{\mu}V_{\nu})(\partial^{\mu}V^{\nu})+\frac{1}{2}(\partial_{\mu}V^{\mu})(\partial_{\nu}V^{\nu})+\frac{1}{2}m^2V_{\mu}V^{\mu}
We are then going to use the Euler-Lagrange...
Thanks for your insight. I'm not able to see, however, how it is the ang. mom. that's incorrect. The -i still comes from the mom. in the hamiltonian and cancel the i in the ang. mom.
Anyway, I'm still having trouble finding out where that ang. mom. actually came from, I haven't been able to...