Efeito Aharonov-Bohm sem interação com a fronteira do solenóide

• Ano de defesa: 2013
• Autor(a) principal: Romano, Renan Gambale
• Orientador(a): Oliveira, César Rogério de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• País: BR
• Palavras-chave em Português: Física matemática; Campos magnéticos; Confinamento quântico
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/5891

One of the biggest problem in the mathematical modeling of the Aharonov- Bohm Effect is the interaction between the electron and the solenoid border. Such interaction translates into boundary conditions on that border, which causes great ambiguity because in principle it is not clear what the most appropriate choice. In quantum mechanics this conditions represent self-adjoint extensions of the Schrödinger operator of the problem. On the other hand, recent works has demostrated that it is possible to confine quantum particles in certain regions of Rn with magnetic fields sufficientily intense near the border of that region. Mathematically this corresponds to essentially selfadjoint Schrödinger operators, which means exemption from the particle interation with the solenoid border In this work we intend to combine the two situations mentions above to study the Aharonov-Bohm effect in the plane, adding then external magnetic fields and potentials that are suffiently intense in the solenoid border so that the related Schrödinger operator is essentially self-adjoint.