Background
Pair production is the opposite of annihilation. Mysteriously, particles can appear from nowhere. Matter is created from an energetic photon (gamma ray).
In the pair production process, a photon is absorbed and a particle and its anti-particle appear, such as an electron and a positron pair. Energy is conserved, keeping with the laws of physics, as the photon must be equal to or greater than the sum of the two particle energies. However, it is incredibly strange that two particles can randomly appear. This only happens in the quantum world. Two objects in the visible world that we see would never disappear and appear randomly.
Explanation
When particles annihilate, their wave centers remain. The particles are still there, occupying space, if you consider the particle to be its physical wave centers. However, the particles no longer have a standing wave structure. The combined amplitudes are zero due to destructive wave interference. They can no longer be detected by electromagnetic apparatus and they no longer have standing wave energy that would be measured as mass.
The particles (or at least their wave centers) do continue to exist and will remain locked together until a photon with sufficient energy strikes the particle/anti-particle pair. When it does, the energy is transferred from transverse form back to longitudinal, standing wave form. The particles (such as the electron and positron) appear again, seemingly from nowhere.
They were always there, just in a different form.