Imprimitively generated Lie-algebraic Hamiltonians and separation of variables

Details Imprimitively generated Lie-algebraic Hamiltonians and separation of variables Imprimitively generated Lie-algebraic Hamiltonians and separation of variables

1998-06-11

arxiv.org/abs/solv-int/9806003v1

Mathematics

Differential Geometry

32 pages. To appear in the Canadian Journal of Mathematics

Scientific paper

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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