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Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrödinger equations. (English) Zbl 1080.35105
Summary: Separable coordinate systems are introduced in 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 Schrödinger equation in the separable coordinate systems are computed.

MSC:
35Q40PDEs in connection with quantum mechanics
81Q05Closed and approximate solutions to quantum-mechanical equations
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