Including both electric and magnetic potentials

The presence of a magnetic field can be included in the so-called minimal coupling by addition of a vector potential A to the momentum operator p, forming a generalized momentum operator jt, which for an electron (charge of -1) is given by eq. (8.21). 

The magnetic field is defined as the curl of the vector potential. 

For an external magnetic field, it is conventional to write the vector potential as in eq. (8.23). 

With the generalized momentum operator n replacing p, the time-independent Dirac equation may be separated analogously to the procedure in Section 8.2.1 to give the equivalent of eq. (8.13). 

In contrast to the situation without a magnetic field, the latter vector product no longer disappears. The ti x ti term can be expanded by inserting the definition of 7i from eq. (8.21). 

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