The various orientations of orbital angular momentum and spin give rise to the fine structure of atomic spectra. This is known as spin-orbit coupling or LS. Russal Saunders coupling, L-s coupling, J-J coupling, Spin orbital coupling. In quantum mechanics, the procedure of constructing eigenstates of total angular momentum . becomes small. For an extensive example on how LS-coupling is practically applied, see the article on term symbols. (\boldsymbol{. This description, facilitating calculation of this kind of interaction, is known as jj coupling.‎General theory and · ‎Spin-orbit coupling · ‎Spin-spin coupling · ‎Term symbols.


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If two or more physical systems have conserved angular momenta, it can be useful to combine these momenta to a total angular momentum of the combined system—a conserved property of the total system.

The building of eigenstates of the total ls coupling and jj coupling angular momentum from the angular momentum eigenstates of the individual subsystems is referred to as angular momentum coupling.

Application of angular momentum coupling is useful when there is an interaction between subsystems that, without interaction, would have conserved angular momentum.


By the very interaction the spherical symmetry of the subsystems is broken, but the angular momentum of the total system remains a constant of motion. Examples[ edit ] As an example we consider two electrons, 1 and 2, in an atom say the helium atom. If there is no electron-electron interaction, but only electron-nucleus interaction, the two electrons can be rotated around the nucleus ls coupling and jj coupling of each other; nothing happens to their energy.

Both operators, l1 and l2, are conserved.

Angular momentum coupling - Wikipedia

However, if we switch on the electron-electron interaction that depends on the distance d 1,2 between the electrons, then only a simultaneous and equal rotation of the two electrons will ls coupling and jj coupling d 1,2 invariant.

Given the eigenstates of l1 and l2, the construction of eigenstates of L which still is conserved is the coupling of the angular momenta of electrons 1 and 2.

The perturbation Hamiltonian is again proportional to the scalar product of the two vectors: Naturally, an atom with a nuclear spin of zero does not show any hyperfine structure splitting, and the hyperfine interaction ls coupling and jj coupling strongest for s-electrons due to their non-zero probability density inside the nucleus - this is known as the Fermi contact interaction.

That concludes this overview of atomic physics. Using perturbation theory in order of diminishing severity, we have added layers of complexity to the structure of the atom.

As a result, a series of splittings of previously degenerate energy levels arises. We have used the vector model of angular momentum to understand how spin and orbital angular momentum couple and how the structure of complex atoms is affected by this.

Thank you very much! Spin-orbit coupling is about a relativistic effect over an MOVING electron and its interaction between the spin and the potential.

LS coupling is mostly having a Hamiltonian where L and S are not conserved and you need to write your system in a different base. I was wrong Zeeman effect alone is not enough for LS coupling.

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