# 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} }

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…

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