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Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schr\H{o}dinger equations

E. G. Kalnins·Z. Thomova·P. Winternitz
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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 Schr\H{o}dinger equation in the separable coordinate systems are computed.

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E. G. Kalnins, Z. Thomova, P. Winternitz. 2004-05-26. Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schr\H{o}dinger equations. https://doi.org/10.2991/jnmp.2005.12.2.4

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