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Author Kalnins, E. G. ♦ Kress, J. M. ♦ Miller Jr, W.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-02-12
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Mathematical Physics ♦ 20C35 ♦ 20C99 ♦ math ♦ physics:math-ph
Abstract We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal coordinate system. As examples we treat two potentials with parameter k (one of which is the Tremblay, Turbiner, and Winternitz system) that have been shown to be classically superintegrable for all rational numbers k. We apply the canonical operator method to give a constructive proof that each of these systems is also quantum superintegrable for all rational k. We also develop the classical analog of the quantum canonical form for a symmetry. It is clear that our methods will generalize to other Hamiltonian systems.
Educational Use Research
Learning Resource Type Article
Page Count 25


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