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 Mar 14 comment Exact energies of spherical harmonic oscillator in Dirac equation @Jakub, Here is a notebook where I am trying to test the formula: nbviewer.jupyter.org/gist/certik/c0d8dc5417fc579d6158, it doesn't seem to work, also it doesn't contain the constant $c$. However, the equation (21) looks promising, but it also seems to give wrong energies. Maybe I implemented it incorrectly in the notebook. The energies I posted above should be correct, I checked those using a shooting method as well as finite elements. Jul 28 comment Need to Zero Angular Momentum My understanding is that you want to find a rotating frame of reference such that the angular momentum is zero in it (there should be just one such frame). Then you want to know the velocities in this frame of reference. May 27 awarded Popular Question 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?