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It is obvious that a source which behaves as an inert object throughout the
experiment is sufficient for the single particle treatment. Indeed, let us
examine
where Ψ, χ and φ denote the full wave function, the source's wave
function and that of the traveling electron, respectively. If the traveling
electron is described by 2 sub-packets then the general form of the full
wave function is
Now, if the source behaves as an inert object then
and the source's wave function is factored out as shown:
The Tonomura experiment uses a source which is a
single domain of a ferromagnetic material.
The inner structure of this magnet is certainly not affected by the
fields of the traveling electron. Hence, the source behaves as an inert
object throughout the process and the AB phase shift is obtained.
On the other hand, it can be shown that if the electric AB effect holds then
energy conservation is violated.
For a discussion,
Click here.
Another case is the magnetic AB effect. Here, if the single domain is
replaced by an appropriate classical source then the magnetic AB effect
disappears.
For a discussion,
Click here.
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