Hi George,
you are perfectly right, my question does not makes sense without specifying the observer's motion with respect to the photon. So I guess the correct answer is Ich's:
f=-u_a k^a=-g_{ab}u^bk^a ,
because it takes into account that. However, I am curious about the quantity...
Hi Ich,
thank you for your answer.
This is the point: I would like to know what is the energy of the photon in a generic system of coordinates in which the metric is described by g_{\mu\nu} . Is it g_{ij}P^iP^j? (sum is over spacial indexes)
Is the implicit summation over 0,1,2,3 or...
Hi atyy,
thank you for your answer!
The link seems very interesting. However, I was hoping you could point some intuitive physical argument, not a mathematical one.
Cheers,
G.
Hi everybody!
I am wondering, among other things, whether the Special Relativity relationship E = p for a photon (I am using c = 1 units ) is still valid in General Relativity.
Let me explain my question in detail. By applying the null geodesic condition with a diagonal metric, we obtain...
Hi Everybody!
I am raising this post from the dead just to list a few algorithm I used with success to integrate the above function:
1) Andrew Hamilton's FFTLog algorithm from http://casa.colorado.edu/~ajsh/FFTLog/. It permits you to integrate not only f(x)*sin(x) but any integrand in the...
Hi mathman, thank you for your answer. You are right indeed.
I tried to expand the sine & cosine as my first approach, but I made a stupid mistake in the calculation of the coefficients and I got wrong results. I re-did everything and now I get results as precise as 10^-6. Thank you...
I forgot to mention that I need to compute the functions for a very large array of "r" values from within a C++ program. Thus, pasting the result from Mathematica is not helpful :)
Cheers,
Guido
Hi everybody!
I kindly request your help. I have to compute functions like
\frac{ \sin (r x) - r x \cos (r x)}{r^3}
(primitive function of x sin(rx) )
or
\frac{ -r x (120 - 20 r^2 x^2 + r^4 x^4) cos(r x) +
5 (24 - 12 r^2 x^2 + r^4 x^4) \sin(r x)}{r^7}
(primitive function of x^5 sin(rx) )...
uart, thank you very much for the idea! This way I can evaluate the integral almost analytically.
I am trying a slightly modified version of your approach by using a Splines interpolation of f(k) instead of a linear one; I will let you know the outcome. By the way, do you have any idea on how...
Hi,
did I omit some important information? Or maybe I posted in the wrong forum?
By the way, I found a routine in the GNU Scientific Library called "QAWF adaptive integration for Fourier integrals" that could be what I am looking for. I only need to get acquainted with GSL, and it is going...
Hi everybody!
I kindly request your help in optimizing the numerical integration of the following expression:
\xi (r)=\frac{1}{2\pi ^2}\int_{-\infty}^{\infty}f(k)\cdot \sin(k\cdot r)\cdot dk
f(k) vanishes outside the boundaries k=0 and k=2; I have got k and f(k) as float arrays, so we...
Hello everybody!
I was wondering if something like NRC Rankings exist also for European Grad Programs. In particular, I would really like to find a ranking (or merely a list) of the best Astronomy-Cosmology Grad Programs in UK-France-Spain-Italy-Portugal.
By the way, I suggest...
I found your assertion
an eye opener, so I tried to deduce it using the Heisenberg Uncertainty Principle.
Correct me if I'm wrong!
Let's think of the particle-particle collision in terms of the collision parameter b (the minimum distance the two protons would be in a collision if the...
Hi Eye_in_the_Sky,
Thanks for the answer! I thought about the diffraction pattern, but I don't think it's the case.
In fact, my teacher was talking about a gas of protons at very high temperature. Precisely, the context was an exercise that required calculating the temperature at which protons...
Am I corrent in assuming that, with the statement
you mean that, for a fairly localized wavepacket, \Delta x \simeq \lambda ?
If the answer is "Yes", wouldn't that imply that the momentum has to be similar to his incertainty?
In fact, \Delta x \Delta p \geq \frac{\hbar}{2} \quad...
Thanks for the answer.
I understand my mistake on differentiating, but how do you justify the fact that we cannot localize the particle with precision greater than \lambda?
In the free particle case
\Delta x\geq\lambda since \Delta x=\infty;
but what about a bound particle?
Guido
Localization vs De Broglie wavelength
First of all, I would like to say hello to everybody since this is my first post, even if it's been some time since I read Physics Forums.
Second, sorry for my bad English, I'm Italian :)
Third, the issue:
I read from my teacher's notes, that a...