The normal Zeeman effect ↩

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created: 2022-01-06 06:52:14
modified: 2022-01-10 04:13:03

For the hydrogen atom

The Hamiltonian operator for the hydrogen atom in a constant magnetic field:

Where the magnetic field is chosen to be parallel to the -axis, is the -component of the angular momentum operator, and is the charge and mass of the electron. The used system is GCGS.

is the Hamiltonian of the hydrogen atom:

Whose eigenfunctions are and the energy levels are proportional to .

How does the total Hamiltonian act on ?

Thus, the eigenstates of the hydrogen atom are also eigenfunctions of with the following energy eigenvalues:

Where is the Larmor frequency:

The magnetic field removes the -fold degeneracy of the energy levels. A level with angular momentum quantum number is split into equidistant levels. The magnitude of the splitting is:

The splitting leads to additional transitions, which however are restricted by the selection rule . This equidistant splitting caused by the magnetic field is called the normal Zeeman effect.

In many-electron atoms, refers to the total angular momentum and to the corresponding quantum number.