GLOBALISM OF COMMUTATION RELATION AND MECHANISM OF MOMENTUM-TRANSFER IN THE AHARONOV-BOHM EFFECT

After examining the domain of an operator that has classical analog, w hich is shown to be the whole spatial space, the concept of globalism of a commutation relation is introduced through analyzing the quantiza tion of the kinetic angular momentum in the Aharonov-Bohm effect. Its applications are also given to explain in an elegant and precise way, the mechanism of momentum transfer in the Aharonov-Bohm scattering and to study the probability distribution of the momentum for a particle in a one-dimensional infinitely deep square potential well.