Superintegrability on the two-dimensional hyperboloid | Zendy

E. G. Kalnins | Zendy; Willard Miller | Zendy; G. S. Pogosyan | Zendy

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Superintegrability on the two-dimensional hyperboloid

Author(s) -

E. G. Kalnins,

Willard Miller,

G. S. Pogosyan

Publication year - 1997

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.531951

Subject(s) - hyperboloid , mathematics , coordinate system , variable (mathematics) , symmetry (geometry) , quadratic equation , separation of variables , polynomial , point (geometry) , basis (linear algebra) , quantum , pure mathematics , algebra over a field , mathematical analysis , geometry , physics , quantum mechanics , boundary value problem

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

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