O princípio de ação quântica de Schwinger: aspectos do tratamento de sistemas dependentes do tempo e interagentes
This thesis has the aim of using the Schwinger Quantum Action Principle to study and characterize two kind of quantum systems: the ?rst one is a forced harmonic oscillator whose parameters explicitly depend on time and the second one, a set of harmonic oscillators which interacts linearly. We show f...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Brasil |
| Recursos: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.unesp.br:11449/108902 |
| Acesso em linha: | http://hdl.handle.net/11449/108902 |
| Access Level: | acceso abierto |
| Palavra-chave: | Teoria quântica Osciladores harmônicos Teorema de Noether |
| Resumo: | This thesis has the aim of using the Schwinger Quantum Action Principle to study and characterize two kind of quantum systems: the ?rst one is a forced harmonic oscillator whose parameters explicitly depend on time and the second one, a set of harmonic oscillators which interacts linearly. We show for the ?rst system that the functional form of this principle, i.e. the operator which causes the generalized variations of the dynamical variables of the system, besides allowing the construction of transformation functions of any kind of system, help to determine the associated conserved quantities and therefore to deduct the form of the spectrum and the set of the eigen-functions of the system, if they exist. Otherwise, if the system is time-dependent, the dynamical algebras which allows studying it in an alternative way can be constructed. Similarly, for the second system two sets of states and operators are proposed. The ?rst one associated with the quantum state of each element of the system in the presence of interaction, known in the literature as Dressed States and the second one, which represents the normal modes of the system as a whole. Both sets of states are used in the implementation of the Quantum Action Principle allowing to ?nd the exact solutions, the spectrum, wave functions and amplitudes between any two states in which the system can be found. In each case, a few examples will be given and the results are contrasted with results associated with other theoretical approaches |
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