Blueshift of an Electron in Amplitude Splitting Interference

We consider a single electron amplitude splitting interference experiment with respect to the possibility of a blueshift in energy/momentum due to the changes in static electric potential. This paper is a restatement of a previously published paper1 with a simplified approach to analysing the theory and experimental proposal. The over-all presentation is a straightforward analysis of amplitude splitting interferometry with single electrons and a theoretical discussion of the possible blueshift in energy that the electron undergoes in this preparation. We consider the preparation of a single electron interference effect which uses an electron beam splitting and recombination apparatus and two detectors. The ideal optical interferometer of this form is that which would be referred to as the Mack-Zehnder interferometer. In electronics this idealized form of amplitude splitting interferometry is the Marton interferometer. We assume a standard amplitude splitting interferometer for single electrons as is depicted in Figure 1. This illustration assumes the use of two beam splitters (BS) which would be appropriate for optics, but realistically in the case of electronics we would be using a different apparatus. The interferometer has two outputs which will have light-port/dark-port statistics when the interference is at a central maxima due to a zero phase difference in the two paths. This configuration of the interferometer is the only consideration that is analysed in the current document. The mathematical analysis that we will provide is a treatment of the energy of electric potential for each electron due to the static fields of all other electrons in the beam. In electron interferometry this potential is usually not considered because it is negligible. The typical assumption in quantum mechanics is that the interaction of successive electrons within the beam is of insufficient strength to disturb the single electron states of the beam because the interaction strength is too weak to affect the states of the electron. This is a necessary assumption in single electron interferometry because th