Atomic orbital shapes — eigenfunctions of angular momentum on the sphere
Spherical Harmonics Y_l^m
Spherical harmonics Yₗᵐ(θ,φ) are the angular part of solutions to Laplace's equation on the sphere. They describe atomic orbital shapes in quantum mechanics.
l = angular momentum quantum #
m = magnetic quantum # (|m|≤l)
Surface: r = |Yₗᵐ(θ,φ)|
Color: sign/phase of Yₗᵐ
l0
m0
Orbital names
Nodes0
Drag to rotate. Blue=positive, red=negative lobe. These shapes determine how electrons arrange in atoms.