In a series of notes, it was seen that Einstein’s 1905 energy momentum equation E2 = p2 + m2 (1) can be written as an eigenvalue equation linear in E, p and m. This equation applies to particles and leads to zitterbewegung results which appear in the literature. [ In a note, it was seen how the 2x2 matrix eigenvalue equation was general and could be applied to a photon moving in the y direction in a frame moving along the x axis with speed v. It was then argued that zitterbewegung should be applied to photons as well. In this note, we try to investigate this further. In addition, we attempt to clarify x and y direction motion of photons and their relation to the 2x2 model. We also examine zitterbewegung in EM energy density equations such as: energy density= .5(E2 +B2) and try to apply it to the cases of a photon moving in the y direction in a box moving in the x direction and to a photon moving in the x direction in a similar box. In such cases, the E field carries effects of the translational motion which are part of the zitterbewegung.
The selection rule which forbids $J=1\ensuremath{\leftrightarrow}0$ two-photon decay when the energies of the two photons are equal is shown to apply only when the multipolarities of the two photons are the same (i.e.,
2E1,
2M1, etc.) and does not generally apply to mixed multipolarity amplitudes such as
E1M2. A calculation of the two-photon decay rate for He-like ions in the
23S1 state including both
2E1 and
E1M2 two-photon decay amplitudes is presented. It shows a significant contribution for the case of equal-energy photons. The ratio of the
E1M2 contribution to the
2E1 contribution is found to be surprisingly large. For example, it is 0.27 for two-photon decay of the
23S1state in He-like uranium.