Recent content by Lancen

Yes the Laughlin wavefunction is a trial wavefunction for many interacting electrons, I understand that much. What I am trying to do is make the connection from the wavefunctions to how this relates to seeing the quantized plateaus in the hall resistance and why the resistance goes to zero as...

Can someone explain to me as simply as possible why the Laughlin states create energy gaps in the lowest landau level? I am trying to understand for a presentation why the Laughlin states correctly model the QHE effect when the filling factor is a odd fraction (1/3, 1/5, 1/7). As far as I...

Yes I realized that too earlier today but then why is that same thing not also done with the dk1 and dk2 integrals? Also if you look a bit further up at the example of the simple massless scalar field in 1D the integral over dk (no subscript) this is equation 2.17, is explicitly from 0 to...

Hello I am trying to work out the Casimir force via the Abel-Plana equation. I have been following the derivation in http://arxiv.org/abs/quant-ph/0106045. Specifically I can't figure out for the life of me how the author is going from the first part of equation 2.33 to the second part of...

Suppose I had a uniformly charged sphere of some density, inside this sphere at some position there is a cavity of some radius. If I wanted to then find the Electric field somewhere, like say the surface of the sphere, how would I approach the problem? Heres what I did. I pretended the cavity...

I have a problem that involves computing the vector surface of z=e^(1-x^2-y^2) where z is greater then or equal to 1, for a Vector Field F=xi+yj+(2-2*z)k. This is to be done using Gauss' theorem. I got an answer of 0, which doesn't seem right I just want to ask if anyone can confirm or deny the...

I been busy the last few days and haven't had a chance to take a look at these forums. How do I find the linearized system? I took another look at the equation and realized it is indeed separable!

I have a problem regarding the equations dx/dt=x-xy and dy/dt=y+2xy. I need to find the critical points of this system and denote if they are stable or asymptotic or whatever. I flipped through the section on this and you can find the critical points by setting dx/dt and dy/dt to zero and...

Ah, I see. I have one more problem with the question. If the disc is upright and is free to roll without slipping along the surface on which it rests under gravitational forces, what's the period T for small oscillations about the vertical position? I am having a bit of trouble understanding the...

I got that far. I know the cut out hole is presented as "negative" mass, but the problem is Ip = Icm + M*h^2 = M*L^2+M*h^2=1/2((pi*a^2*v)-pi*(a/2)^2*v))*L^2+((pi*a^2*v)-pi*(a/2)^2*v)*(5a/6)^2. Here Icm is the rotational inertia about the center of mass C which is not at the center of the...

I am having problem with a relatively simple problem that I probably have done before but because my Physics have become so rusty recently I just can't get the right answer. You have a disc that sitting about some point P on the ground - so its upright - and there is a hole cut out on the top...

I am still a bit confused but I have something like this - (xn,yn) = (8,6)+[(-3x,2y)/sqrt(36x^2+4y^2)]*[v,w] where (xn,yn) is the new point after moving some distance, [v,w] the unit vector and [(-3x,2y)/sqrt(36x^2+4y^2)] the gradient divided by its length to give you the unit gradient, but how...

Sorry I don't quite follow, the negative of the directional derivative is the directional I need to go, but what is the parametrized curve? Is the equation of setting up -M(x,y)=(x(t),y(t))?

This is a problem that's been bugging me. Suppose you are on the surface M(x,y)=3*x^2+y^2+5000 that describes a magnetic field, you are at the point (8,6), what is the curve along which you should travel so as to minimize field intensity as rapidly as possible? I am told I need to solve a...

Bump, anyone?