Hydrogen atom wavefunctions |ψₙₗₘ|² in cross-section
1s orbital
Scale1.5
Brightness2.0
Hydrogen wavefunctions are ψₙₗₘ(r,θ,φ) = Rₙₗ(r) · Yₗᵐ(θ,φ). The radial part uses associated Laguerre polynomials; the angular part uses spherical harmonics. This visualizes the probability density |ψ|² in the x-z plane (cross-section). n gives the energy shell, l the orbital shape (0=s, 1=p, 2=d, 3=f), and m the orientation. The Bohr radius a₀ ≈ 0.529 Å sets the length scale.