The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra

Abstract

The family F of all potentials V(x) for which the Hamiltonian H in one space dimension possesses a high order Lie symmetry is determined. A sub-family F', which contains a class of potentials allowing a realization of so(2,1) as spectrum generating algebra of H through differential operators of finite order, is identified. Furthermore and surprisingly, the families F and F' are shown to be related to the stationary KdV hierarchy. Hence, the "harmless" Hamiltonian H connects different mathematical objects, high order Lie symmetry, realization of so(2,1)-spectrum generating algebra and families of nonlinear differential equations. We describe in a physical context the interplay between these objects.

15 pages, LaTeX

Cited by in corpus (5)

• Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
• New infinite families of $N$th-order superintegrable systems separating in Cartesian coordinates
• Two-dimensional superintegrable systems from operator algebras in one dimension
• Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras
• Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates