Recent content by pdxautodidact

Generally dark matter is described as a halo, which would be a sphere around the galaxy.. If the majority of the dark matter around the Milky Way is present at its boundary, then its much, much farther than the distance to the sun (LY vs. AU). The standard cosmological model is lambda CDM...

I don't think I am explaining myself clearly, but I am good now. Thanks!

I think I see what you mean. I was worried because I remember a professor teaching that a system with negative energy indicates a bound system. Also, because conservative forces must satisfy ##-\vec{\nabla}V=\vec{F}##, I thought the sign surely must not be arbitrary (although one can naturally...

But for a bound system energy should be negative, like the electron in the hydrogen atom. You do the same thing, but with Coulomb Force. The potential for that force is negative, so it is more than the kinetic energy term and you're left with negative energy which is ##-\frac{R}{n^2}##, where...

Still getting a positive energy, if anyone sees any flaws in my methodology please post! Thanks & cheers.

My mistake was using a minus sign in my force; the centripetal force should have had a minus sign too. I used $\hat{r}$ for my force, but not with the centripetal force, which would also be negative. I should have just used the magnitude. The exponent k isn't specified as odd or even, so we...

Homework Statement Use the Bohr quantization rules to calculate the energy levels for a particle moving in a potential \begin{equation} V\left(r\right)= V_0 \left(\frac{r}{a}\right)^k \end{equation} where k is positive and very large. Sketch the form of the potential (done) and show that the...

Yeah, I combined the trig terms into a 0 instead of a 1, so that's it. I see why it works for all cases now, in hindsight it's obvious. Thanks!

Okay, so I went through it again: let X be the 2 sphere with your suggested parameterization $$ X_{;\theta} = \left( \begin{array}{c} x^1 = rcos\theta cos \left(\phi + \theta \right) - rsin \theta sin \left(\phi + \theta \right) \\ x^2 = rcos \theta sin \left( \phi + \theta \right) +...

Does that, in fact, parameterize a sphere? It's not obvious to me. I included an r term in the coordinates since I want it in general, not the only the unit case. The induced metric was: $$ \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & r^2 sin^2\theta & r^2 sin^2\theta \\ 0 & r^2...

So, by accident, while deriving the induced metric for a sphere in 3 dimensions I realized that the transpose of the jacobi matrix multiplied by the jacobi matrix (considering it as 3 row/column vectors)will work out the induced metric. Why is it that i≠j ends up being superfluous. One would...

hi both & thanks, i don't meen a new gauge groupn (except the dark U(1)), merely to look at strongly interacting particles in addition to weakly interacting particles. I'm not in graduate school or academia, and it's been a few years since I've been reading papers, so I'm a little out of the...

Well, coupling a dark radiation component has been done: "http://arxiv.org/abs/0810.5126. Can one make an SU(3) coupling to dark matter, intead of the standard SU(2) isospin route. The arguments I hear for WIMPS are that they interact only via the weak nuclear force, thus they happen...

Is anyone familiar with a $$ SU\left( 3 \right) \otimes U \left( 1 \right){}_d$$ or $$SU \left( 3 \right) \otimes SU\left( 2 \right) \otimes U \left( 1 \right)_d $$ model? Kind of what I'm currently interesting in working with, but I don't have access to anything other than the arxiv.cheers.

So, I just went through the derivation of the Lie algebra for SO(n). in order to do so, we considered ##b^{-1}ab##, and related it to ##U\left(b^{-1}ab\right)##, and since we have a group homomorphism, ##U^{-1}\left(b\right)U\left(a\right)U\left(b\right)##, all of which correspond to the...