Minimum Barrier Height That Produces a Resonance

This thesis is concerned with a research project that aims to investigate the minimum barrier height that produces a sharp resonance by combining a square well potential with a square barrier potential. This combination is a simple quantum mechanical system. Yet, it deserves a thorough investigation. We deal with this elementary problem based on an advanced quantum mechanical technique i. e, analytically continuable perturbation theory. Before the systematic application of the analytically continuable perturbation theory, however, we need to orient ourselves to the entire project, determining the range of parameters in which thorough investigations must be carried out. A sufficient number of case studies are presented in this thesis. The solutions of the Schrodinger equation have been surveyed in a Wide range of ~meters with the help of the Sigma-9 computer. The behavior of phase shift and cross section as a function of energy has been studied for different combinations of the well and barrier. Finally by studying the shape of resonance peak, with three different values of barrier parameters, we have determined what kind of square well to be combined with each barrier in order to produce a typical case of sharp resonance