Zeeman Effect

The Zeeman effect is the splitting or shifting of quantum energy levels in an applied magnetic field. The basic mechanism is coupling between a magnetic moment and the field. In atoms and molecules, orbital angular momentum, spin, fine structure, hyperfine structure, and selection rules determine the observed pattern.

Formula Hook

The generic magnetic-dipole coupling is

$$H_Z = - \boldsymbol\mu\cdot\mathbf B.$$

For a simple angular-momentum model with magnetic moment proportional to $\hat{\mathbf J}$ and field along $z$,

$$H_Z = - \gamma B\hat J_z, \qquad \Delta E_{J,M}^{(1)} = - \gamma B\hbar M.$$

Atomic spectroscopy often writes a weak-field level shift as

$$\Delta E = g_J\mu_B B\,m_J,$$

with sign conventions absorbed into the definitions of the magnetic moment and the quantum numbers.

Canonical Home

This glossary entry is the compact named-effect home. Generic degenerate splitting, quadratic corrections, and method selection belong to Zeeman Effect as a Perturbation Example. Atomic Landé patterns, the Breit–Rabi crossover, polarization, and spectroscopic inference belong to Zeeman Effect in Atoms. For nearby site material, see Zeeman Effect Revisited, Rotor in External Fields: First Encounter, Degeneracy Lifting, and Particle in a Uniform Magnetic Field.

Common Confusions

• There is no one universal Zeeman formula; the magnetic moment and coupling scheme must be specified.
• Including spin adds physics not present in a spinless orbital Landau-level model.
• The normal and anomalous Zeeman effects differ because electron spin and spin-orbit coupling matter.
• Strong-field Paschen–Back behavior is not the same perturbative regime as weak-field Zeeman splitting.

Related Entries

• Hamiltonian
• Eigenstate
• Degeneracy Lifting
• Zeeman Effect in Atoms
• Zeeman Effect as a Perturbation Example
• Zeeman Effect Revisited
• Stark Effect

References

• C. J. Foot, Atomic Physics, Oxford University Press, 2005.
• D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018.
• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.