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...
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?
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?
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...
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 =)
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...
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...
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
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...
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...
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...
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...
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...
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...
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...
Homework Statement
In the Berkley physics course E&M book (by Purcell) problem 1.16 is giving me some issues.
A sphere of radius a was filled with positive charge at uniform density \rho. Then a smaller sphere of radius a/2 was carved out, as shown in the figure...
Homework Statement
There is a rectangular prismof uniform mass distribution with lengths of a, b, and c (b>a>c). Calculate it's rotational inertia about an axis through one cornet and perpendicular to the large faces.
Homework Equations
I = \int r^2 dm
r^2 = x^2 + y^2 + z^2
\rho =...
you are forgetting about the tension caused by the rope in your force diagram. Heres what I came up with
\sum F_2 = m_2 a_2 = F_a - F_{f2g} -F_{f21} -T
\sum F_1 = m_1 a_1 = F_{f1} - T
Thanks that was it. This brings up a good point, which i've been doing alot lately. I do all of the major mathematics correctly, but I always make some stupid mistake and get the answer incorrect. How do everyone else deal with making those preventable errors?
Homework Statement
A block with mass m_1 = 2 \textrm{kg} slides along a frictionless table with a speed of 10 m/s. Directly in front of it and moving in the same direction is a block of mass m_2 = 5 \textrm{kg} moving at 3 m/s. A massless spring with spring constant k = 1120 N/m is attached...
Agreed that the book is wrong again? I'm using halladay resnick walker fundamentals of physics. Does anybody know of more errors in the book? I'm not in an actual physics class, I'm just freelancing doing problems in my spare time so the answers in the back are the only way to know I'm...
Homework Statement
A target glider, whose mass m_2 is 350g is at rest on an air track, a distance d =53cm from the end of the track. A projectile glider whose mass m_1 is 590g approaches the target flider with velocity v_{1i} = -75 cm/s and collides elastically with it. The target...
I have run into this problem solving differential equations of this type (they occur often doing momentum problems):
kxy = (y+dx)(x+dy)
where k is constant. I multiply it out to :
kxy= xy + xdx + ydy + dydx
Regroup and :
[tex] \int {kxy} = \int {xdx} + \int {ydy} + \int {dydx} [/itex]...
When problems like this get confusing I always go back to the basics. Draw a force diagram of the ball ascending. You have 2 forces, a gravitational force and a drag force:
\sum F = -F_g - F_f = -mg -kv
There is a caveat, however. The "famous 4" are only used when there is a constant...
I believe that this is incorrect because it assumes that the F_f is conservative, however it is non-conservative. I believe what confused chaos is the use of x in the definition for W_f where they really meant s. If we change the definition of the work done by a non-conservative force to a...
Homework Statement
A 50 kg trunk is pulled 6.0 meters up a 30 degree incline at a constant velocity. The coefficient of kenetic friction is .2. What is a) the work done by the applied force, b) the work done by gravity and c) the work done by the frictional force
I set up my x axis in the...