189 resultados para Duffing oscillator


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Pós-graduação em Biofísica Molecular - IBILCE

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

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Pós-graduação em Física - IGCE

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Pós-graduação em Ciência dos Materiais - FEIS

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Pós-graduação em Matemática Universitária - IGCE

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.

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The study of oscillatory phenomena is an important topic in several areas of knowledge. The understanding and the solution of many problems that scientists and engineers confront nowadays can be formulated, at least as an analogy, in terms of an oscillatory movement. The description of the motion of this nature has remarkable contributions to the mathematical and conceptual formation of the students and for solving daily problems in several areas. In this paper we propose a theoretical and experimental approach involving the phenomenon of harmonic oscillations in two dimensions. Lissajous curves were used as experimental demonstration of the resulting trajectories. These curves were obtained from relatively simple experimental apparatus, which is affordable in most teaching laboratories of physics.

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The Schwinger quantum action principle is a dynamic characterization of the transformation functions and is based on the algebraic structure derived from the kinematic analysis of the measurement processes at the quantum level. As such, this variational principle, allows to derive the canonical commutation relations in a consistent way. Moreover, the dynamic pictures of Schrödinger, Heisenberg and a quantum Hamilton-Jacobi equation can be derived from it. We will implement this formalism by solving simple systems such as the free particle, the quantum harmonic oscillator and the quantum forced harmonic oscillator.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)