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...
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?
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'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...
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 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 =...
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...
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]...
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...
Even though this question deals mostly with arithmetic and geometic series, this notation is used in linear algebra and differential geomety quite a bit so I will inquire of this matter here.
What are the rules for algabreically dealing with sigma notation. When you change the value of an...
I have heard the term moment being used quite often in physics (like a moment in the distributions of mass within closed systems, moments of inerta, as well as torque), but it has never been offically explained to me.
I was attempting to do a problem about the bending of a pliabile beam to one...
It has been about 2 years since i last did calculus but im trying to get back into it so im ready for college / dont kill myself because of boredom
I am having difficulty finding integrals of the form
\int{\frac{x^2}{x+a}dx}
This integral inparticular is:
\int{{\frac{x^2}{2x+2}dx}
I...
I am attempting to teach myself differential geometry (being bereft of creditied educational institutions in my area) and I am being irked by that fact that I do not have a good physical/geometrical view of the exterior derivitive 'd'; which is a necessity of being a visual learner.
Does...
this is my first post on this site but it looks like the sort of ppl that i would like to associate myself with.
Unfourtanately, I have not had any formal schooling for any mathematics above calculus but i have read a few books and papers and am trying to make due.
I was studying about the...