Abstract
The aim of this paper is to show that the vector potential in the so-called Aharonov-Bohm (A-B) effect is not a gauge transformation of the vacuum, even when α = integer(≠0) (where α = Φ/ Φ 0 represents the magnetic flux in the long cylindrical solenoid and Φ 0 = h/ e). To this end, it is discussed that the wave function of the electron and the gauge function in a gauge transformation are required to be single-valued so that the Schrödinger wave mechanics and the Maxwell electromagnetic theory are well-formulated. It is also discussed that the gauge transformation of wave functions and the representation change of operators of Kobe's meaning are the same thing.
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