Método de Runge-Kutta de 4ª ordem para a equação de Schrödinger estacionária com energia zero

Abstract

The Schrödinger equation has been solved numerically by several Runge-Kutta methods. The study of this equation considering the system energy being zero, among several other applications, allows an analysis of the binding limit state of a particle in a given quantum system. Thus, in the present work we solve the equation in its zero mode, considering an extrinsic approach to confinement in a one-dimensional region, using the 4th order Runge-Kutta method most used for ODE solutions. Initially, we obtained numerically the wavefunctions for a particle confined in a straight line and in circles of different radius, as they are curved with parameterizations by arc length file. Then we study curves from their curvatures, which advises the study of confinement in Archimedean spirals and in logarithmic spirals. Finally, we study confinement in hypothetical curves that do not yet have defined parameterizations. The results obtained made it possible to analyze the regions in the curves with greater tendencies to occur ionization, which could be used as model for the ionization of molecules and nanostructures with geometries similar to those studied.