Subgroup Type Coordinates and the Separation of Variables in Hamilton-Jacobi and Schrödinger Equations

E G Kalnins, Z Thomova, P Winternitz
2005 Journal of Nonlinear Mathematical Physics  
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 Schr\H{o}dinger equation in the separable coordinate systems are computed.
doi:10.2991/jnmp.2005.12.2.4 fatcat:2n6uo2yqovejtb4qjwb5qkkcom