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Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables

Published online by Cambridge University Press:  20 November 2018

Robert Milson
Robert Milson*
Affiliation:
McGill University, Montreal, PQ H3A 2K6
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Abstract

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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.

Keywords

35Q4053C3081R05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 6 , 01 December 1998 , pp. 1298 - 1322
Copyright
Copyright © Canadian Mathematical Society 1998

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