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arxiv: 1206.2907 · v2 · pith:JK64NFRInew · submitted 2012-06-13 · 🧮 math-ph · math.MP· nlin.SI· physics.class-ph· quant-ph

Particular Integrability and (Quasi)-exact-solvability

classification 🧮 math-ph math.MPnlin.SIphysics.class-phquant-ph
keywords particularintegrabilityoperatorsquasiappearcalogero-sutherlandcaseclassical
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A notion of a particular integrability is introduced when two operators commute on a subspace of the space where they act. Particular integrals for one-dimensional (quasi)-exactly-solvable Schroedinger operators and Calogero-Sutherland Hamiltonians for all roots are found. In the classical case some special trajectories for which the corresponding particular constants of motion appear are indicated.

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