Superintegrability on the two-dimensional hyperboloid

E. G. Kalnins, W. Miller, G. S. Pogosyan

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.

Original languageEnglish (US)
Pages (from-to)5416-5433
Number of pages18
JournalJournal of Mathematical Physics
Issue number10
StatePublished - Oct 1997
Externally publishedYes


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