Hydrogen Electron Orbital Probability Distribution Cross-Sections

Here are some different shapes that a hydrogen atom can take. These plots are based on the same function as the vibrating balloon :
P = 4 π r2ψr2ψθ2, ψr = eρlLn-1-l2l+1(ρ), ψθ = Ylm(θ,φ), ρ = 2r/n
(* runtime: ggg second *)
P[n_, l_, m_, {x_, y_, z_}] := Module[{r = Sqrt[x^2 + y^2 + z^2]}, 4 Pi r^2(Exp[-r/n]r^l LaguerreL[n - 1 - l, 2l + 1, 2 r/n])^2 Abs[SphericalHarmonicY[l, m, ArcCos[z/r], ArcTan[x, y]]]^2];
DensityPlot[P[3, 1, 0, {x, 0, z}], {x, -20, 20}, {z, -20, 20}, Mesh -> False, PlotPoints -> 275, Frame -> False, Compiled -> False]

3 Responses to “Hydrogen Electron Orbital Probability Distribution Cross-Sections”

  1. September 12, 2010 at 1:45 am

    Dear Paul Nylander,

    I very much appreciate your blog and associated some of your ideas with cymatics and water reorientation and skateboarding. I love to skate and find a variety of interests from cymatics, fractals and physcis to cultural appreciation from around the world. I created a post called “Cymatic skateboards and water reorientation” as a liberal and humanitarian art work and scientific challenge to perhaps assist others in the study of hydrology, browns gas, quantum physics, applying fractals in practical engineering, experimenting with ultra violet black light emissions or cymatics as alternatives in wave theory dynamics in a chaotic model for process engineering, etc.

  2. December 18, 2010 at 1:24 am

    Those hydrogen orbitals are beautiful!

    Symmetry and periodicity!

    Have you seen this on-line book?


    Harmonic Resonance is a pretty magical property of physical matter!


  3. 3 Emanuele
    June 21, 2011 at 8:26 pm

    very beautifull…but the link of vibrating balloon doesn’t works ?

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