Recent content by r16

Homework Statement Construct the analytic mapping \phi(x,y) for the H^{2+} \times S^1 representation of SL(2;R) Homework Equations g(x) \circ g(y) = g(\phi(x,y)) The Attempt at a Solution So, all points in SL(2;R) lie on the manifold H^{2+} \times S^1. I also know that SL(2;R) is...
2. Fourier Transforms, Momentum and Position

I'm only starting out in Quantum Mechanics (chapter 2 of the griffiths book) and I am not familiar with the notation I'm sure ill get to it later on in the book. Until then, could you explain it?
3. Fourier Transforms, Momentum and Position

In quantum mechanics, why does the Fourier transform f(x) = \int_{-\infty}^\infty F(k) e^{ikx}dk represent position and F(k) = \int_{-\infty}^\infty f(x) e^{-ikx} dx represent momentum?
4. Three suns in the sky Believe it or not

To drag this discussion away from physics into the occult, the ancient mystics believed in 3 suns: the first represents the material world governed by the gnostic demiurgus (in Christianity the holy spirit), the second the light of intellect which is governed by Lucifer (the evils of intellect...
5. Normalization of a Wave Function

i did the integral mathematically exactly the way you said! I wasn't completely sure that this was the correct way to evaluate the absolute value, but I had a feeling it was. I'm a math major in addition to being a physics major =)
6. Normalization of a Wave Function

Homework Statement I'm starting to (trying) teach myself some quantum mechanics out of the Griffiths book, and since there are no answers in the back I have no idea if I'm on the right track or not. Could you guys look over the answer to this equation to see if it looks right? Consider the...
7. What is vacuum?

I like your idea about before the big bang we say there was nothing, but in a vacuum there is nothing, so how does a vacuum differ from before the universe began? From that definition the vacuum definitely does exist as SOMETHING-it does have an energy associated with it, possibly a structure...
8. What is Energy?

wow that story sounds pretty hardcore. I was thinking about it, and you could define energy simply as the ability to do work, but then your stuck with the question again, what is work
9. What is Energy?

I've been throwing this term energy around for a while now, and thinking about it I have absolutely no idea what it is. Is it something that actually exists in the universe, or just a construct that we use to simplify problems? Terms like kinetic energy, and even gravitational potential...
10. Energy in a Capacator with a Diaelectric

wow thats quite an elegant proof, i really like it. by \rho I assume you mean the free charge, since, \nabla \mathbf{D} = 4 \pi \rho_f i guess this is what is confusing me: why are you able to ignore the effects of the bound charge? The energy stored in the capacator is stored in terms...
11. Energy in a Capacator with a Diaelectric

Ok, I think I remember seeing that equation some where, however it was not in my book. Is there a link to a good derivation of this equation? With this, the answer is trivial. Where I learn the most, however, is having someone explain to me how what I was doing was incorrect. Could anyone...
12. Energy in a Capacator with a Diaelectric

Homework Statement I was attemping to solve problem 10.13 in Purcell's E&M Book: By considering how the introduction of a dielectric changes the energy stored in a capacitor, show that the correct expression for the energy density in a dielectric be \frac{\epsilon E^2}{8\pi} Homework...
13. Electric Field in a Non-symmetric Sphere (Purcell 1.16)

I like thinking things through quite thoroughly and i often over complicate, ive been dealing with this issue for as long as i can remember I'm confused, isn't a charge density of -ρ different than there just being no charge in there at all? Wouldn't this just make a dipole-moment-ish...
14. Gauss's Law

rgr that, opening up my book and looking at it again, I see what you are saying. I guess I am having difficulty imaging an electric field and calculating values for an electric field especially when it comes to asymmetric shapes, such as an electric field in an unsymmetrical hollowed out...
15. Gauss's Law

I was thinking about gauss's law and ran into this contradiction. Consider this situation in electrostatics. You have an infinite line of charge, uniform charge density [text]\lambda[/tex]. In cgs units, E at a distance r from the line of charge along the +y axis (assuming a left handed...