Separation of Variables
Open Access
- 1 January 1995
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics Supplement
- Vol. 118, 35-60
- https://doi.org/10.1143/ptps.118.35
Abstract
The review is based on the authro'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 constructuion 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 Schrödinger equation, SL(3)-invariant magnetic chain. New results for the 3-particle quantum Calogero-Moser system are reported.Keywords
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