Poço quadrado quântico finito e método de fatorização

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

O formalismo supersimétrico e suas aplicações em mecânica quântica

Pós-graduação em Biofísica Molecular - IBILCE

Estudos de confinamento quântico em ligações de hidrogênio

Pós-graduação em Biofísica Molecular - IBILCE

Estados ligados em mecânica quântica relativística

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equação de Fokker-Planck, supersimetria e enovelamento de proteína

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Momentos fracionários e localização dinâmica para o modelo de Anderson discreto multidimensional

Pós-graduação em Matematica Aplicada e Computacional - FCT

Mecânica quântica supersimétrica: aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Potenciais periódicos: aplicação à espectroscopia do benzeno

Pós-graduação em Física - FEG

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem