Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrődinger equations

Abstract

Separable coordinate systems are introduced in the complex and real four-dimensional flat spaces. We use maximal Abelian subgroups to generate coordinate systems with a maximal number of ignorable variables. The results are presented (also graphically) in terms of subgroup chains. Finally, the explicit solutions of the Schrődinger equation in the separable coordinate systems are computed.