## 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