# Recent content by coccoinomane

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...