Spherical Harmonics and Atomic Orbital Shapes

This visualization demonstrates how the shapes of atomic orbitals up to g orbitals are related to spherical harmonics, which are solutions to the angular part of the Schrödinger equation.


  1. The 3D plot shows the shape of the spherical harmonic \( Y_{l,ml}(θ,φ) \) for the selected quantum numbers n, l, and ml.
  2. These shapes represent the angular part of the wavefunction \( ψ \), which is a solution to the Schrödinger equation for hydrogen-like atoms.
  3. The radial distance from the origin represents the absolute value of the spherical harmonic \( |Y_{l,ml}(θ,φ)| \).
  4. The shapes correspond to the probability density of finding an electron in different regions around the nucleus.
  5. Notice how different combinations of n, l, and ml produce various shapes, including cloverleaf-like patterns for certain d and f orbitals.

Quantum Numbers: