# Ondřej Čertík

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bio website ondrejcertik.com location Los Alamos, NM age 30 member for 2 years, 3 months seen Jan 28 at 20:47 profile views 77

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 Feb28 awarded Popular Question Nov29 revised How to derive inverse Fourier transform for periodic functions (in crystal lattice)? Fix a typo: instead of 0, it should be oo Nov29 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. Nov29 answered How to derive inverse Fourier transform for periodic functions (in crystal lattice)? Nov28 revised How to derive inverse Fourier transform for periodic functions (in crystal lattice)? Added a reference to the other derivation Nov28 revised Simplest derivation of Fourier transform for periodic functions (in crystal lattice)? Add a note about proper definition of G Nov28 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. Nov28 answered Simplest derivation of Fourier transform for periodic functions (in crystal lattice)? Nov28 asked Simplest derivation of Fourier transform for periodic functions (in crystal lattice)? Nov27 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. Nov26 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.) Nov26 asked How to derive inverse Fourier transform for periodic functions (in crystal lattice)? Apr23 awarded Nice Question Apr22 revised Exact energies of spherical harmonic oscillator in Dirac equation Add the value of omega that was used to obtain the numerical results. Jan30 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. Jan30 answered Why does isotropy principle require existence of inertial transformation when axes are reversed? Jan16 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). Jan15 accepted Determination of auxiliary scale in dimensional regularization Jan15 asked Why does isotropy principle require existence of inertial transformation when axes are reversed? Jan5 comment Exact energies of spherical harmonic oscillator in Dirac equation natan, I created another bounty if you are interested.