A cloud of possible outcomes.
Every luminous point is an independent sample drawn from |ψ|². Dense regions are more likely measurement outcomes. The rendering is not a swarm of electrons and shows no hidden trajectory.
Analytic eigenstate
Equation Lab / Atomic physics
The shape of possibility.
A hydrogen orbital is a wavefunction, not an electron’s path. Change the quantum numbers and explore a Monte Carlo rendering of the exact nonrelativistic eigenstate in three dimensions.
03 / Radial probability
Where a measurement may land.
P(r) = r²|Rnℓ(r)|² gives the probability per unit radius after every direction is included. Empty spherical gaps mark radial nodes—not forbidden classical shells.
No radial nodes in this state.
Normalized radial distribution0 — 30 a₀
Color belongs to the wave.
In the complex basis, color encodes arg(ψ). In the real basis, the two dominant colors mark opposite signs. Phase drives interference; it is not electric charge or a measured color.
An ideal hydrogen atom.
This is the normalized, nonrelativistic single-electron Coulomb solution with no external fields, spin structure, fine structure, Lamb shift, or relativistic correction. Those effects split energies but do not turn orbitals into paths.