# Search results

1. ### Photon/particle's energy in General Relativity

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...
2. ### Photon/particle's energy in General Relativity

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...
3. ### Photon/particle's energy in General Relativity

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.
4. ### Photon/particle's energy in General Relativity

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...
5. ### Numerical integration - Fourier transform or brute force?

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...
6. ### Roundoff error - double precision is not enough

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...
7. ### Roundoff error - double precision is not enough

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
8. ### Roundoff error - double precision is not enough

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) )...
9. ### Numerical integration - Fourier transform or brute force?

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...
10. ### Numerical integration - Fourier transform or brute force?

Hi Dr.D, thank you for the answer. The function f(k) vanishes for k<0 and k>2, so the infinite integration limits should not be a problem.
11. ### Numerical integration - Fourier transform or brute force?

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...
12. ### Numerical integration - Fourier transform or brute force?

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...
13. ### Academic and Research Programs in Science, Math and Engineering

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...
14. ### Localization vs De Broglie wavelenght

Now everything is clear (al long as QM can be clear :smile: )! Thanks a lot for the explanations, Guido
15. ### Localization vs De Broglie wavelenght

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...
16. ### Localization vs De Broglie wavelenght

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...
17. ### Localization vs De Broglie wavelenght

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...
18. ### Localization vs De Broglie wavelenght

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
19. ### Localization vs De Broglie wavelenght

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...