In the homework on electrons in an electromagnetic field, we showed that
**the Schrödinger-Pauli Hamiltonian gives the same result as the non-relativistic Hamiltonian we have been using
and automatically includes the interaction of the electron's spin with the magnetic field**.
The derivation is repeated here.
Recall that
,
, and that the momentum operator
differentiates both
and the wavefunction.

We assume the Lorentz condition applies.
This is a step in the right direction.
The **wavefunction now has two components** (a spinor) and the effect of spin is included.
Note that this form of the NR Hamiltonian yields the coupling of the electron spin to a magnetic field
with the **correct factor of 2**.
The spin-orbit interaction can be correctly derived from this.

Jim Branson
2013-04-22