The terms are positive energy plane waves and the states are ``negative energy''. The differing signs of the energy in the time behavior will give rise to rapid oscillations.

The plane waves can be purely either positive or ``negative energy'', however,
**localized states have uncertainty in the
momentum and tend to have both positive and ``negative energy'' components**.
As the momentum components become relativistic, the ``negative energy'' amplitude becomes appreciable.

Even the Hydrogen bound states have small ``negative energy'' components.

The cross terms between positive and ``negative energy'' will give rise to very rapid oscillation of the expected values of both velocity and position. The amplitude of the oscillations is small for non-relativistic electrons but grows with momentum (or with localization).

Jim Branson 2013-04-22