This paper presents the derivation and applications of the variable phase equation for single channel quantum scattering. The approach was first presented in 1933 by Morse and Allis and is based on a modification of the Schrödinger equation to a first order differential equation, appropriate to the scattering problem. The dependence of phase shift on angular momentum and energy, together with Levinson's theorem, is discussed. Because the variable phase equation method is easy to program it can be further explored in an introductory quantum mechanics course. Keywords: phase equation, scattering matrix, phase shift.Este artigo apresenta a dedução e aplicações da equação da fase variável para o caso de um canal no espalhamento quântico. Esta abordagem foi apresentada pela primeira vez em 1933 por Morse e Allis e baseia-se numa modificação da equação Schrödinger para uma equação diferencial de primeira ordem, adequada para o problema de espalhamento. A dependência do deslocamento de fase com o momento angular e a energia, juntamente com o teorema de Levinson,é discutida. A equação resultante do método da fase variávelé de fácil programação e pode ser explorado em cursos introdutórios de mecânica quântica. Palavras-chave: equação da fase, matriz de espalhamento, deslocamento de fase.

Metallic complexes of multimetal and multiligand systems are complicated for calculating equilibrium concentrations in solutions. An artificial neural network has been developed for studying Al 3+ and EDTA complexes in solution with an initial concentration of 0.01 mol L −1 for these species. In this system there are 20 compounds and may exist 18 simultaneous reactions. The neural network has been trained and the simulated data of different concentrations as a function of pH are predicted with an accuracy of about 1% for all species simultaneously. A general analytical formula is presented, which directly relates all the concentrations as a function of pH. The analysis showed that predictions closer to the boundary of the input and output data are quantitative while out of these limits these are not even qualitative.

Recebido em 8/6/11; aceito em 10/11/11; publicado na web em 31/1/12Potential parameters sensitivity analysis for helium unlike molecules, HeNe, HeAr, HeKr and HeXe is the subject of this work. Number of bound states these rare gas dimers can support, for different angular momentum, will be presented and discussed. The variable phase method, together with the Levinson's theorem, is used to explore the quantum scattering process at very low collision energy using the Tang and Toennies potential. These diatomic dimers can support a bound state even for relative angular momentum equal to five, as in HeXe. Vibrational excited states, with zero angular momentum, are also possible for HeKr and HeXe. Results from sensitive analysis will give acceptable order of magnitude on potentials parameters.