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… 

New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates

A study is presented of superintegrable quantum systems in two-dimensional Euclidean space E 2 allowing the separation of variables in Cartesian coordinates. In addition to the Hamiltonian H and the

Classification of separable superintegrable systems of order four in two dimensional Euclidean space and algebras of integrals of motion in one dimension

A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta. All quantum

Two-dimensional superintegrable systems from operator algebras in one dimension

We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on

References

SHOWING 1-5 OF 5 REFERENCES

A new class of Hamiltonians with so(2, 1) as spectrum generating algebra, International Center for Theoretical Physics

  • Trieste Report IC/75/112,
  • 1972

Transformation groups applied to mathematical physics

I: Point Transformations.- Introductory Chapter: Group and Differential Equations.- 1. Continuous groups.- 1.1 Topological groups.- 1.2 Lie groups.- 1.3 Local groups.- 1.4 Local Lie groups.- 2. Lie

Dynamical Groups and Spectrum Generating Algebras

This book contains an up-to-date review on dynamical groups, spectrum generating algebras and spectrum supersymmetries, and their application in atomic and molecular physics, nuclear physics,

Applications of lie groups to differential equations

1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and