Nondegenerate superintegrable systems in n-dimensional Euclidean spaces

We analyze the concept of a nondegenerate superintegrable system in n-dimensional Euclidean space. Attached to this idea is the notion that every such system affords a separation of variables in one of the various types of generic elliptical coordinates that are possible in complex Euclidean space. An analysis of how these coordinates are arrived at in terms of their expression in terms of Cartesian coordinates is presented in detail. The use of well-defined limiting processes illustrates just how all these systems can be obtained from the most general nondegenerate superintegrable system in n-dimensional Euclidean space. Two examples help with the understanding of how the general results are obtained.