Recent content by Chen

I'm studying a course in Fourier. In a multi-choice question, one of the answers asks for the value of the definite integral of sin(ax)/x over [-pi,pi]. I am wondering if there is a way to calculate this integral (I guess using Fourier techniques) or not. It is possible that it can't be solved...

Please see here: http://www.youtube.com/watch?v=n5bsQ_YDYCI&feature=player_embedded# First - wow. Second - I'm not sure I understand the mathematician's explanation. Why would there be a thin layer of air to begin with? Is this correct? Is there a different explanation for this...

If I knew what I wanted to hear I wouldn't need to ask you for it. Can you please give others a chance to answer my question as well? I thank you for your answer but I want to hear other possible answers.

Ok. Maybe someone else can provide a different explanation.

Thanks, although that's not derived from Fermi's golden rule is it... I was hoping for a more intuitive explanation. Pressure broadening stems from enhanced stimulated emission, doppler broadening is obvious... where does the natural linewidth comes from?

Well, doesn't it give the wrong result for the lineshape (sinc and not Lorentzian)?

Hi, I am trying to understand exactly how and why the lifetime, or decay rate, of an atomic level determines the spectral width of the transition to this level. Also I would like to understand why the natural lineshape is a Lorentzian. I am familiar with the vague explanations involving...

Thanks. But I know how to calculate this with Biot-Savart's law. I want to know where the application of Ampere's law to this problem fails.

There is a formula here: http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/MagneticField/MFStraitWire.html If we limit our discussion only to the center of the wire, theta=phi and you obtain the result of an infinite wire, times cos(theta). And I am not at all sure where in Ampere's law this...

Let's say I want to calculate the magnetic field at a distance d from the center of a wire of finite length L, carrying a current I. Why would it be wrong to apply Ampere's law to a circular path of radius d centered on the wire, and say that the integral of B.dl is simply B times 2pi*d...

Yes that would be correct, a bad case of dullness. Thanks.

After a bit of search I see that the method to solve this kind of recurrence relations is to assume a solution of the form A \lambda_1^N + B \lambda_2^N and find A and B from the initial conditions. However this is not exactly the form of the solution here... how come?

Hmm, pardon my ignorance, but what does that wedge stand for? Thank you

Hi, I'm reading a paper where the determinant of the following matrix is solved for using some kind of recurisve method. The matrix is given by M_{ij} = A \delta_{i,j} - B \delta_{i,j-1} - C \delta_{i,j+1}, with i,j = 1...N and are NOT cyclic. The author sets D_N =...

To give a concrete example to my last question, take a look here, at the second identity: http://www.pact.cpes.sussex.ac.uk/~markh/Teaching/RQF3/node22.html (this is actually exactly what I'm dealing with)