A quantum mechanical particle with the spin (no angular momentum) and a charge unequal tozero has a magnetic moment , where is the gyromagnetic ratio.

Within a magnetic field the magnetic moment undergoes a curl free force [1]. Thus it is possible to introduce a potential. In the case of a magnetic field , homogeneous and constant in time, the magnetic moment has the additional potential energy:

where is the spin operator, is the normalised eigenfunction and s₃ the corresponding eigenvalue. The spin is quantised i.e. s₃ is a discrete value, which leads to a discrete set of possible energy levels.

For example a proton can have two possible spin alignments corresponding to the values s₃=. This results in two energy levels which differ by

Bibliography:

1. Kap. Stationäre Ströme, Magnetostatik In: Lindner, A.: Grundkurs Theoretische Physik, Teubner Studienbücher Physik, 1994, S.202