The Hydrogen Atom — Orbital Shapes and the Blurred Electron Cloud

An electron in the Coulomb potential V = −e₀²/4πε₀r created by a single proton. Solving the Schrödinger equation in polar coordinates gives ψ = R_nl(r)Y_lm(θ,φ), from which 1s, 2s, 2p, 3s, 3p, 3d, … emerge. In ① you see the blurred electron itself, and in ② you see its shape.

All lengths are in units of the Bohr radius a_B = 4πε₀ħ²/m_ee₀² = 52.918 pm.