Separation of Variables. New Trends.

Details Separation of Variables. New Trends. Separation of Variables. New Trends.

1995-04-04

arxiv.org/abs/solv-int/9504001v1

Prog.Theor.Phys.Suppl.118:35-60,1995

Nonlinear Sciences

Exactly Solvable and Integrable Systems

33 pages, harvmac, no figures

Scientific paper

10.1143/PTPS.118.35

The review is based on the author's papers since 1985 in which a new approach to the separation of variables (\SoV) has being developed. It is argued that \SoV, understood generally enough, could be the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer function can be interpreted as a variant of \SoV, and moreover, for many particular models it has a direct quantum counterpart. The list of the models discussed includes XXX and XYZ magnets, Gaudin model, Nonlinear Schr\"odinger equation, $SL(3)$-invariant magnetic chain. New results for the 3-particle quantum Calogero-Moser system are reported.

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