Construção e propriedades de uma família de hamiltonianos de Dirac auto-adjuntos no intervalo finito

• Autor(a) principal: Santos Junior, Emanuel Vieira dos
• Data de Publicação: 2019
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: http://ri.ufs.br/jspui/handle/riufs/13087
• topic: Física; Ensino de Física; Hamiltoniano de Dirac; Condições de contorno auto-adjuntas; Espectro; Completeza; Dirac Hamiltonian; Self-adjoint boundary conditions; Spectrum; Completeness; CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL

This work deals with the study of the one-dimensional Dirac Hamiltonian in a finite interval. Was applied von Neumann theory of self-adjoint extensions of symmetric operators to determine the existence of a four-parametric self-adjoint family of Dirac hamiltonians. For the construction of the self-adjoint hamiltonians of this family, was applied the AIM (Asorey, Ibort, Marmo) formalism where we explicitly determine the form of the boundary conditions. Using these boundary conditions we obtain the equation that defines the particle energy spectrum and the explicit form of the eigenfunctions for all the members of the four-parametric family. Was discussed the peculiarities of the problem that consists in the existence of the states with energy less than rest energy, edge states. Was graphically demonstrated the dependence of the energy of edge states for some biparametric classes of the family. For the sets of the eigenfunctions of the four-parametric family of hamiltonians, the orthogonality relationship was explicitly demonstrated and the scheme of the proof of completeness of the sets of the eigenfunctions was presented.