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Hydrogen Atom Wavefunctions

Probability density |ψ_{n,l,m}|² in the x-z plane. The wavefunction is ψ = R_{nl}(r) · Y_l^m(θ,φ). Radial part uses associated Laguerre polynomials; angular part uses real spherical harmonics. Units: Bohr radii (a₀ = 0.529 Å).

ψ(3,0,0) — 3s orbital

Darker = higher probability density. Nodes (zero crossings) appear as dark bands. The number of radial nodes = n − l − 1; angular nodes = l. Energy E_n = -13.6/n² eV depends only on n.