Spin (physics) - Spin Quantum Number

Spin Quantum Number

As the name suggests, spin was originally conceived as the rotation of a particle around some axis. This picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta:

• Spin quantum numbers may take half-integer values.
• Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower.
• The spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the internal charge of the particle were distributed differently from its mass.

The conventional definition of the spin quantum number s is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 0, 1/2, 1, 3/2, 2, etc. The value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum S of any physical system is quantised. The allowed values of S are:

where h is the Planck constant. In contrast, orbital angular momentum can only take on integer values of s, even values of n.