Free electron case

The simplest case is that of an unpaired electron, with quantum number S=1/2.

For this system there is a magnetic moment μ associated with the spin S which is oriented by the magnetic field because of the Zeeman interaction. For this quantum system the projection of the magnetic moment along the field is quantized; the quantization is given by the quantum number ms.

Zeeman splitting for a S=1/2 system

where g is the gyromagnetic factor of the electron.

A transition between the two levels can be induced by a radiation that fulfil the requirement:

Resonance phenomenon in EPR

A continuous wave (cw) EPR spectrum is normally acquired by measuring the absorption of microwaves while sweeping the magnetic field. Most EPR spectrometers use lock-in detection, and the spectra are in derivative form.