Jens
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 May 2 reviewed Close Unintended effect of closing square bracket on Spanish keyboard in Mathematica online May 2 comment Complex valued 2+1D PDE Schrödinger equation, numerical method for NDSolve? @user21 The answer is yes, but it's a vast subject. Some good and reasonable simple applications could be found in physical chemistry and mesoscopic physics (picking some fields at random). Or maybe I don't know what you mean by "application". The better question is perhaps: where are ideal 2D rectangular geometries ever found in applications? Most applications don't have the symmetries of the rectangle. Apr 30 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? Apr 30 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). Apr 30 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. Apr 30 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. Apr 30 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. Apr 29 awarded Enlightened Apr 29 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. Apr 29 revised NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity Added explanations Apr 29 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. Apr 29 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 29 awarded Nice Answer Apr 29 revised NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity Boundary condition at the origin Apr 29 answered NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity 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.