Jens
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 1d comment Mirror image of a point about a line It's not clear what you're asking. Are you asking about the maths or the software Mathematica? 1d comment Eigenelements of conductivity equation It would probably be easiest to separate variables in polar coordinates and impose the matching condition after obtaining the general solution in the two regions (they are Bessel functions). 1d comment Mirror image of a point about a line Please post the Mathematica code you have tried, and point out where exactly you have difficulties. 1d comment Complex valued 2+1D PDE Schrödinger equation, numerical method for NDSolve? @user21 Maybe you'd be interested in this Mathematica Journal article by Michael Trott: The Sound of an Unusual Drum - if you haven't seen it already. 1d comment Complex valued 2+1D PDE Schrödinger equation, numerical method for NDSolve? @user21 I don't think I understood the question. Are you saying that there is a way to impose boundary conditions with TensorProductGrid? Maybe using that method instead of FEM in your answer here? I don't know of anything that's been posted on SE that would come close to what you did in the linked post. From there, constructing time-dependent solutions would be straightforward by fitting a superposition of eigenstates to the initial condition. 2d comment NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity @MatthewBrunetti I've tried to add most of these comments to the answer as introduction. 2d comment NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity So yes, I think it's better for numerical stability to avoid the reduced wave function here, because of the issues at $m=0$. The $m\neq 0$ radial functions vanish at $r=0$ just like the reduced ones, just with a different power. The transformation of variables is indeed mainly for improved accuracy and speed, as mentioned in the linked question. It compresses the boring large-$r$ region into a smaller interval. 2d comment NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity Yes - I'm using the full radial wave function to avoid the $1/4$ modification that causes a diverging potential at $m=0$. You can verify that I'm not adding a $\sqrt{r}$ in the plots. The problem at $m=0$ is that your original formulation had a centrifugal barrier that wasn't strong enough (due to the $1/4$) to suppress amplitudes fully at $r=0$ so that the divergence clashed with the Dirichlet boundary condition in a region where it's numerically hard to get the amplitude (it's a numerical, not a "fundamental" problem, hence the dependence on MaxCellMeasure). Apr 28 comment Learning Mathematica for Math Majors You may also be able to get some material from @David, if he's reading this. Apr 28 comment Output short denominator as pre-factor @MichaelE2 Only checked this Q out today - your deleted answer looks very useful! It could be added to \$POST to automate it. And maybe a condition on the ratio of LeafCounts could be added. Apr 27 comment determine frequencies This question could also be interpreted as taking the 2D FT of an image. I know it's not the most likely interpretation, but we're not mind-readers, so you'll have to be more specific and show what you have tried. Apr 26 comment Drawing spheres with texts on top of each other without overlapping Maybe what you mean is this: “Covering up” text in Graphics. This describes alternatives to the Text command you're using. Text in 3D always displays in front of everything, and seems to be what really causes the issue you want to avoid. Apr 26 comment Drawing spheres with texts on top of each other without overlapping I don't understand why you want to plot three objects on top of each other. What is the real purpose ? What are you trying to manipulate? Why not hide the spheres you don't want to be seen? It could easily be automated and would be faster, too. Apr 25 comment NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer It's worth pointing out that the l=0 case was the topic of a previous question. You could probably adapt my answer using the coordinate transformation to this case. Apr 24 comment Solving wave PDE I think the question was unclear about the initial condition. It's probably supposed to be u[x,0] == 5 - Abs[x-5] to get a triangle shape. I would have voted to close it if you hadn't already put in the work... Maybe you could try it for this more physical initial condition instead. Apr 23 comment Core functions or operations that every aspiring Mathematica programmer should know? It would be helpful to readers if the target audience is narrowed down from generic "programmer" - e.g., are you coming from Matlab or R or do you mainly do image processing, or linguistics, or interactive demos, or 3D modeling, or numerical differential equations (just some random directions that come to mind)? It's hard to fit a catch-all answer into the format of this site. Apr 19 comment Lagrangian to Hamiltonian This is the simplest answer, but it hasn't kept me from adding a more complicated alternative which may be of interest in more general situations. Especially for people who don't remember the definitions and don't want to look them up... Apr 18 comment Custom operator form for system functions? How about Infix notation? It looks nice for your example: Range[10]~RandomSample~3. No need to Unprotect anything. Apr 17 comment How to make this beautiful animation I think I've managed to find the source of the animation and added it to the question. In searching for it, I saw how rampant it is to rip off original art like this. Apr 17 comment How can I create a graphic of a wedge of a cylinder (like a slice of pie)? I made a function that can do that as part of this answer. It's called ellipse3D