Recent content by qasdc

Sorry for my late reply and thank you for another very informative post. I have been aware of most of what you mention in your last post, except for the formula: [f, F(f,g)] ~=~ \frac{\partial F}{\partial g} [f,g] ~=~ [f,g] \frac{\partial F}{\partial g} Normal ordering, for example, is...

Thank you both for your replies. strangerep, your reply is much more than I hoped for. Sorry for not mentioning that I am interested in the case where canonical commutation relations hold. So let me sort things out. First of all, the definition of the derivative that I provided above, should...

Jano L. , thank you for your answer. However, I do not understand what your point is. The definition of the above derivative is very clear and the result you got for H(p,q) = q + pq - qp is the correct one since, \begin{equation} H(p,q) = q + pq - qp = q - [q,p] = q - i \hbar...

Let my rephrase my question to make things a bit simpler. Suppose that you have an equation, \begin{equation} \frac{\partial H}{\partial q_1}(q_1 ,..., q_n)=1 \end{equation} where the derivative is defined according to my previous post. Would that imply that, \begin{equation} H(q_1 ...

"Integration" on operators Hi! I am having some difficulty in finding a definition about some kind of reverse operation (integration) of a derivative with respect to an operator which may defined as follows. Suppose we have a function of n, in general non commuting, operators H(q_1 ,..., q_n)...

I found it. Using the following definition of the delta function: \lim_{\epsilon \rightarrow 0} \frac{1}{\sqrt{\epsilon}}e^{-\frac{t^2}{4\epsilon}} =2\sqrt{\pi}\delta(t) we find that, =\frac{1}{4r} \lim_{\epsilon \rightarrow 0} \frac{\sqrt{\pi}}{\sqrt{\epsilon}}\int_{-\infty}^{\infty}dt...

So, \int_{0}^{\infty} dk K_{0}(kr)=\frac{1}{r}\int_{0}^{\infty} dx K_{0}(x)=\frac{1}{r}\int_{0}^{\infty} dx \int_{0}^{\infty} dt \frac{\cos (xt)}{\sqrt{t^2 +1}}= =\frac{1}{4r}\int_{-\infty}^{\infty} dx \int_{-\infty}^{\infty} dt \frac{\cos (xt)}{\sqrt{t^2 +1}}=...

fzero thank you for your reply. Yes, I need to do the intergal step by step, otherwise I could get it from mathematica. The answer I get form mathematica is \frac{\pi}{2r} In your reply, I suppose that the first term in each exponential is - \epsilon t^2 rather than - \epsilon x^2 . How...

Homework Statement I need to evaluate the following integral: \int_{0}^{\infty} dk K_{0}(kr) , where K_{0}(x) is the modified Bessel, using the integral representation: K_{0}(x)=\int_{0}^{\infty} dt \frac{cos (xt)}{ \sqrt{t^2 +1}} Homework Equations The Attempt at a Solution

You are right, it's just peak frequency

turin, 2) yes but what does "central frequency" means and how do I calculate it? 3) If you check Jackson (3rd edition page 668), t' refers to the moving particle's own time.

Homework Statement An electron moves in a helix : \vec{r}(t)=v_{z}t \hat{z}+a e^{i\omega_{0}t}(\hat{x}-i\hat{y}), where a is the radius of the helix and v_{z} the relativistic z-component of the velocity. 1) Find the position vector of the electron in a system of reference that is moving...

Ok, thnx! I now understand what was wrong the way I counted.

Hi! I have the following questions and I would like some help. I have N different objects and I choose g out of them (without repetition), avoiding permutations of the objects. This can be done in N!/(N-g)!g! ways. I create another set of g objects in the same way. So, I have two such...