Scientific-Visualization

A collection of scripts for programmatic graphs and scientific visualizations, primarily used in BoosterPrep lectures.

Tools used: Python, Mathematica, and whatever else is relevant.

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Scripts

hydrogen_orbitals.html https://lucasfinney.github.io/Scientific-Visualization/hydrogen_orbitals.html — Zero-install web applet

Hydrogen-like Atom Orbitals

Dependencies: numpy, scipy, matplotlib

hydrogen_orbitals.py — Static multi-panel figure

Generates a publication-ready figure of electron probability densities

ψ_nlm

² in the xz cross-section, grouped by principal quantum number n (one row per n, centred):

Row 1 (n=1):  1s
Row 2 (n=2):  2s   2p(m=0)   2p(m=1)
Row 3 (n=3):  3s   3p(m=0)   3p(m=1)   3d(m=0)   3d(m=1)   3d(m=2)

python hydrogen_orbitals.py              # display
python hydrogen_orbitals.py --save       # save to hydrogen_orbitals.png
python hydrogen_orbitals.py --Z 2        # helium-like ion (He⁺)
python hydrogen_orbitals.py --cmap magma --gamma 0.4
python hydrogen_orbitals.py --help       # full option list

hydrogen_orbitals_interactive.py — Interactive viewer

Dark-themed GUI with live controls. Adjust any parameter and the plot updates instantly.

Control	Range	Description
n	1 – 4	Principal quantum number
ℓ	0 – n−1	Azimuthal quantum number (range updates with n)
m	−ℓ – +ℓ	Magnetic quantum number (range updates with ℓ)
Z	1 – 20	Nuclear charge (1 = H, 2 = He⁺, …)
γ	0.1 – 1.0	Display gamma — lower values reveal diffuse outer lobes
Colormap	—	inferno / plasma / viridis / magma / hot

python hydrogen_orbitals_interactive.py

Note: Grid resolution is set by GRID_SIZE at the top of the file (default 300). Increase to 500–600 for higher-quality screenshots; decrease if updates feel sluggish.