A discretization size and step size varying strategy in the numerical solution of I-Dimensional Schrodinger Equation

In this thesis we present a numerical solution of the I-dimensional Schrodinger equation using the method of lines approach (MOL) where we discretize the spatial dimension using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. We study the effect of changing in the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation. In the study we incorporate the use of Simpson's rule function in MATLAB. The results indicated that there are some advantages in deciding between the discretization sizes or step size in the numerical solution of differential equation as far as the computing time is concerned.