Recent content by Sigurdsson

Sorry for the freakishly late reply. I revisited the book Microcavities again and remembered that I never finished the problem here. Here is my take on it, The solution is as follows: Let's consider the following electric field composed of two plane waves, E = E_0 \left ( e^{-i \omega_1 t} +...

Are the unit vectors ##\hat{e}## and ##\hat{f}## some arbitrary unit vectors in Cartesian space? In that case, it might be easy to start with something simple such as ##\hat{e} = \hat{x}## and ##\hat{f} = \hat{y}## and then moving into a more general case.

Hmmmm... I think I get what you're saying there. If I get terms like \left[ \frac{\partial^n}{\partial x^n} , f(x') \right] then this is automatically vanishes because I'm differentiating with respect to another variable?

Yes yes, this is exactly what I'm wondering about. It's part of understanding why [N,H] = 0 where H = T + V = \int d^3 r \psi^\dagger(\mathbf{r}) T_1(\mathbf{r}) \psi(\mathbf{r}) + \frac{1}{2} \iint d^3r \ d^3r' \psi^\dagger(\mathbf{r}) \psi^\dagger(\mathbf{r}') V_2(\mathbf{r}...

Hi there I've recently started studying quantum field theory and I'm trying to understand the field operators. One thing that bugs me is the difference between field operators and wave mechanics operators. For instance, let's take the kinetic energy operator in wave mechanics for a single...

Getting a little closer, I just realized that the average value of cosine over 2\pi is zero. Meaning... \frac{\langle E^\ast (t) E(t + \tau) \rangle}{\langle |E(t)|^2 \rangle } = \frac{ \langle \left( e^{-ia} + e^{-ib} \right) \left( e^{ia} e^{-i\omega_1 \tau} + e^{ib} e^{-i\omega_2 \tau}...

Homework Statement Hi guys, appreciate all the help I can get. This has been bugging me for 24 hours now. I'm starting to think I'm missing something in the question. We are exploring first-order coherence degree. That is, exploring the coherence of two separate signals (wave packets) by...

Oh, my bad. I thought he was generally stating that quantum particle must be described by a large number of other particles. But this is only his criticism to Verlinde's theory. Thanks guys. :)

I was recently reading a small news article named Experiments Show Gravity Is Not an Emergent Phenomenon. http://www.technologyreview.com/blog/arxiv/27102/?ref=rss. It goes on about gravity not being a traditional force but a emergent phenomenon. But the interseting thing is I've gone...

Right guys so here it is, me and my buddies came up with this solution to the problem. So we have established that our distribution should be g_n(x) = \theta(x - n) - \theta(x + n) Like Vela said, the Fourier transform of this sine resembles our distribution differentiated. So that means...

Thanks Vela! That did the trick, I'll post the full solution later. :)

Homework Statement Find a distribution g_n which satisfies g'_n(x) = \delta(x - n) - \delta(x + n) and use it to prove \lim_{n \to \infty} \frac{\sin{nx}}{\pi x} = \delta(x) Homework Equations Nothing relevant comes up at the moment. The Attempt at a Solution Well the first...

Thanks guys I got it now. The way you laid it out Dickfore makes it really clear but it unnerves me to solve an integral like that using just simple logic. I usually go straight for some rigorous integration rules and tricks instead of just visualizing the problem. Thanks again

You're right, It should be \int_0^y \theta(x - y) dy

Homework Statement Calculate the convolution (\theta \ast \theta)(x) Homework Equations Convolution is defined as: (f \ast g)(x) \equiv \int_{-\infty}^{\infty} f(x - y) g(y) \ dy = \int_{-\infty}^{\infty} f(y) g(x-y) \ dy The Attempt at a Solution I know this is probably easy for...