A wave propagation matrix method in semiclassical theory
Abstract A wave propagation matrix method is used to derive the semiclassical formulae of the multi-turning-point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the process of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. We then apply the method to study scattering by surface transparent potentials and the Bloch wave in solids.
Abstract. One of the goals, in the context of nonparametric regression by smoothing spline functions, is to choose the optimal value for the smoothing parameter. In this paper, we deal with the cross validation method(CV), as a performance criteria for smoothing parameter selection. First, we implement a CV-based algorithm, in Matlab 6.5 medium and we apply it on a test function, in order to emphase the quality of the fitting by the CV-smoothing spline function. Then, we fit some real data with this kind of function.