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In this paper we introduce Schrödinger's operators in a naive and unpretentious way, but with some precision and didactics. The most studied periodic and random potential types are mentioned and, by numerical simulation, compare the eigenvalues of an operator's truncated matrix with a periodic potential and the same potential disturbed by an evenly distributed continuous random variable. We evaluated the magnitude of the random variable required to produce a significant difference between the eigenvalue sets. [ABSTRACT FROM AUTHOR]

In general, data that are obtained by counting processes, strictly discrete or discretized (from truncations and/or rounding), are analyzed, without exhaustion, by the Geometric, Logarithmic, Poisson and Negative Binomial distributions. In recent years a large number of discrete distributions have been proposed in the literature from the discretization of continuous random variables. Many of the discretization methods preserve one or more characteristics of the continuous version, with the proposal of Nakagawa e Osaki (1975) being the most used. In this paper, from this methodology, which makes use of the survival function, we propose the discrete version of the continuous generalized Half-Normal distribution, introduced in the literature by Cooray e Ananda (2008). Some of its properties are discussed and Monte Carlo simulations evaluate the bias and accuracy of the estimates obtained by the maximum likelihood method and method of moments. Some discrete data sets found in the literature are considered to illustrate the applicability of the proposed distribution. [ABSTRACT FROM AUTHOR]