Live in the Cloud — probability samples display; the current switch also needs a rotating-basis state with m > 0, the states that carry one. Full explanation in the notes below.
Each orbital is an electron wavefunction of hydrogen, labeled by the quantum numbers n, ℓ, m.
n (1–6) sets the energy and overall size — higher n, bigger orbital. ℓ (0 … n−1) sets the shape: 0 = s (sphere), 1 = p (dumbbell), 2 = d (cloverleaf), then f, g, h. m (0 … ℓ) is the angular momentum about the vertical axis — it controls how the shape wraps around that axis.
Brightness follows the probability of finding the electron there. Blue marks regions where the wavefunction is positive, red where it is negative. Dark gaps are nodes — surfaces where the electron is never found: n−ℓ−1 spherical shells plus ℓ angular planes or cones.
Some structure hides inside the cloud — the Slice and Cutaway displays expose it, and lowering the brightness thins the cloud.
Rotating states are the true angular-momentum eigenstates: the electron circulates about the vertical axis with definite momentum m, so orbitals with m > 0 appear as symmetric rings around it (the phase rotates; the magnitude shown here does not).
Standing states combine the +m and −m rotations into standing waves — the lobed textbook shapes chemists draw (px, dxy, …). Same physics, different choice of basis.
In the Cloud display, the probe slider softens the position measurement: a Gaussian meter of width σ applied to |ψ|², the continuum between no measurement and collapse. Each measure click draws an outcome from the current posterior and recentres the probe — a few narrow clicks collapse the cloud onto a stochastically wandering point, a quantum trajectory in the sense of continuous-measurement theory.
The current switch shows the Bohmian velocity j/ρ, which is what a weak measurement of momentum returns (Wiseman 2007; Kocsis et al. 2011). Each sample circles the vertical axis at ω = m/(x²+z²): inner rings outrun outer ones, so the cloud shears as it turns. Standing states and m = 0 carry no current — the switch stays off for them because there is nothing to show.