• DOI:10.1063/1.533011
• Corpus ID: 204899723

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

@inproceedings{HDDoebner1998TheSK,
  title={The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra},
  author={H.-D.Doebner and R.Z.Zhdanov},
  year={1998}
}

• H.-D.Doebner, R.Z.Zhdanov
• Published 23 September 1998
• Mathematics, Physics

The family F L of all potentials V ( x ) for which the Hamiltonian H = − d 2 dx 2 + V ( x ) in one space dimension possesses a high order Lie symmetry is determined. A sub-family F 2 SGA of F L , 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 2 SGA and F L 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.