A diversion into hydrogen states.

I made an animated table of hydrogen-state visualizations in Mathematica while putting off a writing assignment. All 35 states from the original collection are here: n = 1 through n = 5, with 0 ≤ l < n and 0 ≤ m ≤ l.

A note on interpretation. These are historical visualization experiments. The original page describes plotting Re(ψ²), which is different from the probability density |ψ|². These shapes should not be read as faithful probability-density plots, and their displayed sizes are not to a common scale.

Original two-dimensional plot for n=1, l=0, m=0; open to inspect the axes
Original two-dimensional plot. Open the image to inspect its axes.
Original three-dimensional visualization for n=1, l=0, m=0
n = 1, l = 0, m = 0 · Rotation paused.
Open the original animations

n = 1
1s, m=0

n = 2
2s, m=0 · 2p, m=0 · 2p, m=1

n = 3
3s, m=0 · 3p, m=0 · 3p, m=1 · 3d, m=0 · 3d, m=1 · 3d, m=2

n = 4
4s, m=0 · 4p, m=0 · 4p, m=1 · 4d, m=0 · 4d, m=1 · 4d, m=2 · 4f, m=0 · 4f, m=1 · 4f, m=2 · 4f, m=3

n = 5
5s, m=0 · 5p, m=0 · 5p, m=1 · 5d, m=0 · 5d, m=1 · 5d, m=2 · 5f, m=0 · 5f, m=1 · 5f, m=2 · 5f, m=3 · 5g, m=0 · 5g, m=1 · 5g, m=2 · 5g, m=3 · 5g, m=4

Download the original Mathematica notebook ↓ · Original hydrogen-state page ↗

Counting fringes, finding wavelengths.

The lab’s custom wavemeter compared an unknown laser with a reference using a scanning Michelson interferometer. My work included electronics fixes, calibration, control-software changes, and a manual documenting the instrument.

For the same change in optical path, fringe count is inversely proportional to wavelength. The reconstruction below follows the ratio in the 2013 manual:

λtest = λreference × Nreference / Ntest

Test wavelength: 914.000091 nm

Illustrative fringe-ratio calculation. It does not apply refractive-index corrections or estimate measurement uncertainty.

Read the preserved wavemeter manual ↗

Modeling the magnetic field.

I used Mathematica to model magnetic dipoles and their images in the Zeeman slower’s housing. The original field animation explores the effect of removing a housing sidewall. The notebook and visualization are preserved below.

The laboratory Zeeman slower assembly
The Zeeman slower, photographed during my undergraduate lab work.
Original modeled magnetic-field cross section of the Zeeman slower housing
Original field model. Open the animated GIF ↗

The original files.

Manuals, notebooks, and drawings from the public lab webpage. These are historical project files, preserved in their original formats.

Retrieved September 6, 2026, from the original resource directory. The notebooks and CAD drawings download as files; they are not executed by this website.

Next: 01.7 / ParseTrail ↗