WAVEFUNCTION ψ

WAVEFUNCTION ψ

An observatory for the hydrogen atom’s stationary states. Every glowing cloud is a real solution of the Schrödinger equation — ψ_nlm(r,θ,φ) built from associated Laguerre & Legendre polynomials — ray-marched in 3D as the probability density |ψ|². The storm of sparks is a live Monte-Carlo experiment: each dot is one simulated measurement of the electron’s position, sampled from |ψ|². Watch the cloud emerge dot by dot, exactly like a real quantum measurement.

QUANTUM NUMBERS

• n — principal (1–7): energy E = −13.6/n² eV and overall size (≈n² a₀).
• l — orbital angular momentum (0…n−1): s, p, d, f, g, h, i.
• m — magnetic (−l…l): tilts and multiplies the lobes.
• Radial nodes = n−l−1 (shells) · angular nodes = l (planes/cones).

TRANSITIONS & PHOTONS

• Change n and the atom absorbs or emits a photon — a coloured streak, a flash, a ping, and a line on the spectrum (Balmer-α 656 nm is the famous red one).
• Electric-dipole selection rule: Δl = ±1. Jumps that break it are forbidden (dim, higher-order) — the log will tell you.
• X cascade: the atom tumbles to the ground state through allowed steps, painting a whole series of lines. (2s is metastable — it decays by two-photon emission!)

CONTROLS

• Space quantum jump · X cascade · T tour · D dots · R ring · C colour mode
• A auto-orbit · P pause · M sound · S snapshot · 1–8 presets
• Colour Phase: cyan/pink = sign of ψ (real orbitals), rainbow wheel = phase arg ψ (complex). Density: pure gold |ψ|². Energy: hue climbs with n.