Aplicación de la mecánica cuántica en el régimen no-relativista para obtener los niveles de energía de un electrón en el efecto Aharonov-Bohm

Abstract

In this degree work, the dynamics of the electron were developed under gauge fields or also called electromagnetic potentials. The importance of potentials in quantum theory was studied and how these are considered more fundamental physical quantities, than the fields themselves. The modification of the dynamics of the electron, caused by the potentials in quantum theory, is known as the Aharonov-Bohm effect. The effect for the magnetic case was raised, that is, in the presence of the potential vector A ⃗, considering the movement of the electron around a small, very long radius solenoid, with a uniform magnetic field B ⃗ inside. For the description of the effect and the importance of the potentials, the electron orbits a region of the solenoid where the magnetic field is zero, but the potential vector is not, at the same time, the bound energy states of the electron were calculated for this case, and like these are modified by the value of the magnetic flux inside the solenoid, flow to which the electron is not exposed. It was explained the meaning of the potential vector appears as a phase factor in the wave function that characterizes an electron, which describes the change in the interference pattern between two electron beams, which pass through the exterior of the solenoid, in a region excluded from fields, but in the presence of the potential vector, which implies that the interference pattern moves on the screen, because the beams arrive with different phases, that difference is represented as ∆Φ. The potential vector is an auxiliary field in classical electrodynamics, however, in quantum mechanics it has physical implications on charged particles. It is recommended for experimental evidence, instruments that generate a magnetic field without leaks, that is, a region excluded from fields. The potential vector is an auxiliary field in classical electrodynamics, however, in quantum mechanics it has physical implications on charged particles. It is recommended for experimental evidence, instruments that generate a magnetic field without leaks, that is, a region excluded from fields.