
The separation of degenerate energy levels into distinct lines, often due to external fields or interactions.Energy level splitting is the phenomenon where a set of degenerate energy levels—states that have the same energy—separate into distinct levels when a perturbation is applied. This perturbation can be an external magnetic or electric field, or an internal interaction such as spin-orbit coupling. The effect is fundamental to quantum mechanics because it reveals the hidden structure of atoms, molecules, and solids. For example, the Zeeman effect splits spectral lines in a magnetic field, and crystal field splitting explains the colors of transition metal compounds and the behavior of impurities in semiconductors.
The Zeeman effect was discovered by Pieter Zeeman in 1896, and the theoretical explanation was provided by Hendrik Lorentz, leading to their joint Nobel Prize in 1902. Crystal field splitting was developed in the 1930s by Hans Bethe and John Hasbrouck Van Vleck.
In an unperturbed system, degenerate states are symmetric and have identical energies. When a perturbation is introduced, it breaks the symmetry, and the states respond differently—some rise in energy, others fall. The magnitude of the splitting depends on the strength of the perturbation and the coupling between the states. In a magnetic field, for instance, states with different magnetic quantum numbers shift by different amounts due to their magnetic moments. In a crystal lattice, the electric field from surrounding ions splits the d-orbitals of a transition metal ion into groups with different energies, depending on their orientation relative to the lattice.
Energy level splitting is exploited in quantum dots for tunable light emission, in rare-earth doped lasers, and in electron spin resonance (ESR) spectroscopy to probe local environments in materials.
The splitting of spectral lines in a magnetic field is so sensitive that astronomers use it to measure the magnetic fields of distant stars—some stars show splittings that imply fields thousands of times stronger than Earth's.




