207 reputation
214
bio website ondrejcertik.com
location Los Alamos, NM
age 31
visits member for 2 years, 11 months
seen Jul 29 at 1:53

Jul
2
awarded  Curious
Feb
28
awarded  Popular Question
Nov
29
revised How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Fix a typo: instead of 0, it should be oo
Nov
29
comment How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Hi Volker, thanks a lot, I think you nailed it! I wrote it up in my answer below. Do you know how to prove ${N_\mathrm{cell}\over\Omega_\mathrm{BZ}}\tilde f(\mathbf{G}+\boldsymbol\omega) =\tilde f(\mathbf{G})\delta(\boldsymbol\omega)$ explicitly? Obviously it's true for $\boldsymbol\omega\ne0$, but I want to make sure all the factors are right for $\boldsymbol\omega=0$ as well.
Nov
29
answered How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Nov
28
revised How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Added a reference to the other derivation
Nov
28
revised Simplest derivation of Fourier transform for periodic functions (in crystal lattice)?
Add a note about proper definition of G
Nov
28
comment How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
@Trimok: just to make it absolutely clear, I've added a new question and answered it myself, where I show in detail how to obtain the $f(\mathbf{x})=f(\mathbf{x})$ identity by substituting the first equation into the second: physics.stackexchange.com/q/88169. Here however I am interested in deriving it from the 3D Fourier transform.
Nov
28
answered Simplest derivation of Fourier transform for periodic functions (in crystal lattice)?
Nov
28
asked Simplest derivation of Fourier transform for periodic functions (in crystal lattice)?
Nov
27
comment How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Thanks @Trimok for the suggestion. Yes, I know how to do that, but as I mentioned in the question, I am interested how to derive it directly from the 3D Fourier transform definition. There must be a way.
Nov
26
comment How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
(@Qmechnic applied the homework tag, that's fine with me --- but it's not a homework, I really want to understand that.)
Nov
26
asked How to derive inverse Fourier transform for periodic functions (in crystal lattice)?
Apr
23
awarded  Nice Question
Apr
22
revised Exact energies of spherical harmonic oscillator in Dirac equation
Add the value of omega that was used to obtain the numerical results.
Jan
30
comment Why does isotropy principle require existence of inertial transformation when axes are reversed?
Hi Luboš, I apologize for my late reply (my son was just born...) and also that I was not clear before, but I finally got back to this. I have posted my own answer, which shows such an experiment. I hope I didn't make a mistake in the derivation, but I am now happy with my own answer, assuming it is correct.
Jan
30
answered Why does isotropy principle require existence of inertial transformation when axes are reversed?
Jan
16
comment Why does isotropy principle require existence of inertial transformation when axes are reversed?
Thanks for the answer and good point about the spatial vector. What you wrote is correct, but I still don't understand why we want to reject such transformations (=how exactly would the anisotropy manifest in physical experiments based on this particular transformation?). This is just a counterexample used in [1] to show that if isotropy of space is not imposed (but you still want linearity and a group), we get this as a possible transformation (there are more such examples, this is just one of them).
Jan
15
accepted Determination of auxiliary scale in dimensional regularization
Jan
15
asked Why does isotropy principle require existence of inertial transformation when axes are reversed?