Sobre a introdução de um operador de translação generalizado na mecânica quântica não-relativística

• Ano de defesa: 2019
• Autor(a) principal: Ferreira, Francisco Ancelmo Pinheiro
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Teoria quântica; Espaço de Hilbert; Osciladores harmônicos
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/39582

In this work we analyze some aspects related to the introduction, in the non-relativistic quantum mechanics,of a translation operator whose action is a function of the point of application. From the introduction of this operator, we derive a modified canonical commutation relation and a modified representation for the momentum operator and we show that such changes require a restructuring of the Hilbert space. We also see that the “new” Hilbert space can be associated with the case of a particle with position dependent mass and also that of a particle moving in a curved space. Still, we compare our formalism with the formalism of von Roos, we analyze the classical limit of this formalism,we solve the problem of a particle with position-dependent mass in two dimensions and we end up analyzing some quantities of information theory for the case of a one-dimensional harmonic particle.