Apresentamos neste artigo duas construções distintas do ensemble ortogonal gaussiano. Para tornar esse trabalho mais didático, usamos as matrizes de ordem dois. Dessa forma, obtivemos analiticamente: a distribuição das matrizes, a distribuição de um elemento da matriz, a distribuição dos espaçamentos, a distribuição de uma componente de um autovetor e a densidade de estados. Para confirmar os cálculos, apresentamos as simulações numéricas.

In this paper we present two distinct constructions of the gaussian orthogonal ensemble. For didactic purposes we consider matrices of dimension 2. In this manner we obtain analytical results for the distribution of the elements of the matrices, the spacing, one component of the wave functions and also the density of states. We compare our analytical results with numerical simulations.

Neste artigo, pretendemos apresentar as aulas sobre o oscilador harmônico amortecido forçado, usando um método geral, para se obter as soluções de equações diferenciais de segunda ordem, não homogêneas. Desta forma, essa contribuição servirá como uma forma de modernizar o tratamento dado em textos conhecidos como os de Symon e Marion. Ele serve também como material didático para alunos do curso de Mecânica I, no segundo ano da graduação do curso de bacharelado em Física. Sugerimos aos alunos interessados que efetuem todos os cálculos passo a passo, para uma melhor compreensão deste trabalho.

In this article, we present ''lectures" about the well-know mechanics problem of a forced damped harmonic oscillator. We use the general method of solving second-order linear, non-homogenous, differential equation. In this fashion our contribuition here should serve to "modernize" the usual textbook treatments of this problem. These lectures can be presented to second year undergraduate students of physics. We suggest that the students go through all the steps used in the derivations.

We consider the effect of the Earth gravitational attraction on nuclear reactions at very low energies. In particular, the Mott oscillation characteristic of scattering of two identical nuclei is found to be slightly but significantly modified. The effect discussed here is different but complementary to the COW effect in cold neutron interferometry. We take as an example 208Pb+208Pb. An angle precision of about 10-3 deg. is required to detect the effect.

The motion of a particle constrained to move between two walls one of which is moveable is solved. We determine analytically the effective forces that act on the particle or on the moveable wall. The quantal version of the solution is briefly discussed.

The nuclear reaction rate formula used in stellar evolution calculation is carefully examined. A uniform expansion is performed up to fourth order in the relevant physical parameter. The convergence of the series is assessed and a semianalytical expression is derived, valid for all values of the expansion parameter. The formulae with electron screening and plasma dissipative collision effects are also evaluated. The agreement of the approximate analytical formulae with the exact result is excellent over a wide range of values of the parameters