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Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables
Published online by Cambridge University Press: 20 November 2018
Abstract
Turbiner’s conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example is given based on the trigonometric Olshanetsky-Perelomov potential corresponding to the ${{A}_{2}}$ root system.
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- Research Article
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- Copyright © Canadian Mathematical Society 1998
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