Superintegrability on the two-dimensional hyperboloid
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Copyright 1997 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp
Abstract
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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Kalnins, E.G., Miller, W., Jr. & Pogosyan, G.S. (1997). Superintegrability on the two-dimensional hyperboloid. Journal of Mathematical Physics, 38, 5416.
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American Institute of Physics