In a classical current loop, torque.

Work required to go from to is

classically

QM

where g is a proportionality constant (=1 for L).

=bohr magneton =

classical electron radius is

g=2 from stern gerlach experiment. Actually, . This can be calculated to almost the same accuracy, and it agrees.

QM derivation:

Hamiltoian in external classical uniform B field:

since , this is

=

where .

Ratio between 2nd and 3rd terms is

source psfile jl@crush.caltech.edu index spin