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

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

2004-05-26

arxiv.org/abs/math-ph/0405063v2

Physics

Mathematical Physics

31 pages, 6 figures

Scientific paper

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.

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