Detalhes bibliográficos
Ano de defesa: |
2014 |
Autor(a) principal: |
Pimentel, Douglas Roberto de Matos [UNESP] |
Orientador(a): |
Não Informado pela instituição |
Banca de defesa: |
Não Informado pela instituição |
Tipo de documento: |
Dissertação
|
Tipo de acesso: |
Acesso aberto |
Idioma: |
por |
Instituição de defesa: |
Universidade Estadual Paulista (Unesp)
|
Programa de Pós-Graduação: |
Não Informado pela instituição
|
Departamento: |
Não Informado pela instituição
|
País: |
Não Informado pela instituição
|
Palavras-chave em Português: |
|
Link de acesso: |
http://hdl.handle.net/11449/111087
|
Resumo: |
The Schrödinger equation for periodic potentials on a ring is approached. For the free rotor, eigenfunctions of the angular momentum operator, as well as eigenfunctions of the parity operator are considered. It is demonstrated that the periodicity of the probability density implies periodic or anti-periodic eigenfunctions. It is shown that the anti-periodic eigenfunctions, because they are discontinuous, or because they have discontinuous first derivatives, are illicit. Then, a few thermodynamic properties of the free rotor are investigated. With a periodic potential V (θ) = V0 (1 − cosNθ) defined on the ring, the problem is mapped in the well-known Mathieu equation with solutions expressed in terms of the eigenfunctions of the parity operator. Again, it is shown that the boundary conditions that make anti-periodic eigenfunctions are illegitimate, reaffirming the results most commonly found in the literature. The low and high energies limits are fully satisfactory. With N = 6 in V (θ), and fulcrum on the Hückel molecular orbital theory, a phenomenological approach to the molecule of benzene is used via the concept of effective moment of inertia in the description of spectroscopy in ultraviolet region |