##

An
System in a Magnetic Field*****

We will derive the Hamiltonian terms added when an atom is put in a magnetic field in
section 20.
For now, we can be satisfied with the classical explanation that the circulating current
associated with nonzero angular momentum generates a **magnetic moment,** as does a classical
current loop.
This magnetic moment has the same interaction as in classical EM,

For the **orbital angular momentum** in a normal atom, the magnetic moment is

For the electron mass, in normal atoms, the magnitude of
is one **Bohr magneton,**

If we choose the direction of
to be the
direction, then the
**magnetic moment term in the Hamiltonian** becomes

So the eigenstates of this magnetic interaction are the eigenstates of
and
the **energy eigenvalues** are
,
, and
.
* Example:
The energy eigenstates of an system in a B-field.*

* Example:
Time development of a state in a B field.*

Jim Branson
2013-04-22