DSpace Coleção:http://ri.ufs.br/jspui/handle/riufs/25602020-07-14T07:55:29Z2020-07-14T07:55:29ZFunções de Green da equação de Schrödinger no intervalo com condições de contorno auto-adjuntas arbitráriasAlves, Matheus Filipe Santoshttp://ri.ufs.br/jspui/handle/riufs/134852020-06-03T00:59:01Z2020-02-07T00:00:00ZTítulo: Funções de Green da equação de Schrödinger no intervalo com condições de contorno auto-adjuntas arbitrárias
Autor(es): Alves, Matheus Filipe Santos
Abstract: This work aims to determine Green functions for the Schr¨odinger equation in the interval with arbitrary self-adjunct boundary conditions. First, von Neumann theory of self-adjoining extensions of symmetric operators was used to determine the existence of a quadri-parametric family of self-adjoining extensions of Schr¨odinger Hamiltonians. AIM formalism (Asorey, Ibort, Marmo) was used to determine the explicit shape of boundary conditions and the construction of the family of self-adjunct Hamiltonians. The scheme of proof of completeness for the sets of self-functions was presented, which is a crucial property for the construction of Green functions. Using the boundary conditions determined by the AIM formalism, Green functions were determined for the Schr¨odinger equation with arbitrary self-adjunct boundary conditions. As an application of these Green functions, the resolving function for this case was found and its veracity was verified by determining the Fourier series by the sets of auto functions of the Schr¨odinger equation for some frequently used cases.2020-02-07T00:00:00ZConstrução e propriedades de uma família de hamiltonianos de Dirac auto-adjuntos no intervalo finitoSantos Junior, Emanuel Vieira doshttp://ri.ufs.br/jspui/handle/riufs/130872020-03-20T11:46:17Z2019-12-13T00:00:00ZTítulo: Construção e propriedades de uma família de hamiltonianos de Dirac auto-adjuntos no intervalo finito
Autor(es): Santos Junior, Emanuel Vieira dos
Abstract: 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.2019-12-13T00:00:00ZObtenção dos Harmônicos Hiperesféricos em N DimensõesSantos, Aleff de Jesushttp://ri.ufs.br/jspui/handle/riufs/128422020-02-28T19:31:28Z2019-12-20T00:00:00ZTítulo: Obtenção dos Harmônicos Hiperesféricos em N Dimensões
Autor(es): Santos, Aleff de Jesus
Abstract: In this work we build hyperspherical harmonics in N dimensions. The Laplace equation in N dimensions in hyperspherical coordinates is obtained using the Laplace-Beltrami operator with the spherical geometry metric. The method used to obtain hyperspherical harmonics is based on the usual method of separating variables and does not involve harmonic polynomial theory, generalized angular momentum theory, or group representation theory. Ordinary equations are reduced to the Schr¨odinger equation with the P¨oschl-Teller symmetrical potential. The solutions of the ordinary equations are presented in the form of the solution of the Schr¨odinger equation multiplied by a functional factor computed in the solution process. Hyperspherical harmonics are obtained as the product of solutions of ordinary equations and are expressed in terms of Gegenbauer polynomials. The result is compared with the results obtained by other methods. For the graphical illustration of the results are presented the images of the projections of the 4-dimensional hyperspherical harmonics in the three-dimensional hyperplanes.2019-12-20T00:00:00ZBusca de assinaturas de jatos em estrelas jovens na Nebulosa da Lagoa (NGC 6530)Castelões, Bárbara SilvaGuimarães, MarceloMcGinnis, Paulinehttp://ri.ufs.br/jspui/handle/riufs/123152019-11-01T19:29:27Z2019-09-06T00:00:00ZTítulo: Busca de assinaturas de jatos em estrelas jovens na Nebulosa da Lagoa (NGC 6530)
Autor(es): Castelões, Bárbara Silva; Guimarães, Marcelo; McGinnis, Pauline2019-09-06T00:00:00Z