Particular Integrability and (Quasi)-exact-solvability

Abstract

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.

13 pages, typos corrected

References in corpus (5)

• Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions
• The quantum $H_4$ integrable system
• The quantum $H_3$ integrable system
• From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model
• Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials. III. $E_8$ case

Cited by in corpus (14)

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• Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions
• On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields
• Two charges on plane in a magnetic field: special trajectories
• From Quantum $A_N$ to $E_8$ Trigonometric Model: Space-of-Orbits View
• Particular superintegrability of 3-body (modified) Newtonian Gravity
• The $B{C}_1$ Elliptic model: algebraic forms, hidden algebra $sl(2)$, polynomial eigenfunctions
• Superintegrability of $(2n+1)$-body choreographies, $n=1,2,3,\dots ,\infty$ on the algebraic Lemniscate by Bernoulli (inverse problem of classical mechanics)
• Two charges on plane in a magnetic field: III. $H{e}^{+}$ ion
• Classical $n$-body system in geometrical and volume variables. I. Three-body case
• Three charges on a plane in a magnetic field: Special trajectories
• Classical $n$-body system in volume variables. II. Four-body case
• $F_4$ Quantum Integrable, rational and trigonometric models: space-of-orbits view