The expected value of a component of the velocity exhibits strange behavior when negative and positive energy states are mixed. Sakurai (equation 3.253) computes this. Note that we use the fact that have ``negative energy''.

The last sum which contains the cross terms between negative and positive energy represents

The Zitterbewegung again keeps electrons from being well localized in a deep potential raising the energy of s states. Its effect is already included in our calculation as it is the source of the Darwin term.

Jim Branson 2013-04-22