O efeito Aharonov-Bohm

Abstract

Published in 1959 by Yakir Aharonov and David Bohm the so named Aharonov-Bohm Effect focus on the importance of vector and scalar potentials in quantum mechanics by proving that these potentials can have more information instead to be used only as mathematical tools. Therefore, in this work we will develop several aspects of Maxwell's equations, including their integral and differential interpretations, to thus obtain the vector and scalar potentials as elementary mathematical processes. Then, by using the gauge transformations, we will obtain the wave equation for the vector and scalar potentials. According to the quantum approach, we will verify the wave nature of quantum particles by analyzing the double slit experiment and its interpretation along the lines of the orthodox interpretation of quantum theory. Finally, we will modify the double-slit arrangement to include a solenoid behind the slits - that do not interfere directly in the path of the electron beam but it makes arise the so called Aharonov- Bohm effect. Finally, we will discuss the real meaning of the vector and scalar potentials in the quantum mechanics context.